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CHILDREN’S ARITHMETICS BY GRADES 


GLOBE SERIES 


Meio i) b OOK 


NUMBERS 


BY 


WILLIAM E> CHANCELLOR, M.A. 


SUPERINTENDENT OF SCHOOLS, BLOOMFIELD, N.J.- 


& 


GLOBE SCHOOL BOOK COMPANY 
NEW YORK AND CHICAGO 


Copyright, 1901, by 


GLOBE SCHOOL BOOK COMPANY. 


Morea. 


“Tf a child learns how to use the text-book, he 
learns how to make use of the experience of 
mankind. The text-book enables the child to do 
individual work for himself, and helps him to 
become independent of oral teaching.” 


Wate wR RIS, 


United States Commissioner of Education. 


MANHATTAN PRESS 
474 WEST BROADWAY 
NEW YORK 


eS ees 


eet MATHEMATICS LIBRARY 
mer 


PREFACE 


For boys and girls who know the numbers from one to ten thor- 
oughly, there is here about a year and a half’s work. 

When should boys and girls begin to study numbers in books? As 
soon as books can help them forward to the mastery of numbers. 
This time comes as soon as children can read. 

How should boys and girls study numbers? The interrelations 
of number-facts and of number-principles are such as to make progress 
very slow and very difficult through their intricate maze. Is there 
any Ariadne’s thread to follow through the labyrinth of numbers? 

Is number ratio or counting? Is it comparison, or magnitude, or 
multitude? Is it a logic of thought, which can be analyzed after the 
topical style, — addition, subtraction, multiplication, division, rule of 
three, and so forth,—of which we may complete one part before 
beginning the next? Shall we learn every discoverable fact about 
twenty before taking up twenty-one, or every conceivable fact about 
4 of § of 3 of 42 before taking up liquid measure? 

‘This book is neither “topical” nor “spiral” in plan. Its substance 
is neither ratio nor counting. Its purpose is to conform numbers in 
their facts and principles to the usual processes and powers and 
interests of children’s minds. The graded reader has opened the way 
for the graded arithmetic. Grading all books is part and parcel of 
the new education, which means to discover and to obey the facts of 
the child-mind, its methods, nascent periods, and order of growth. 

The core of the concentric theory is recognition of the value of 
finding something that is known even in the mass of the unknown. 
Let us not hesitate in schoolbooks as we do not hesitate in life to 
branch out into the new and to return again to the old. Because 
comparing is the root and numbering is the top, let us not forget 
reasoning which is the main trunk of arithmetic. _The child’s knowl- 
edge of arithmetic should grow as evenly in all directions as the most 
careful and the most open-minded education can secure. 

5 


4642433 


6 


Progress in education is largely a matter of progress in power to 
understand books. Oral instruction may be continued too long as 
the sole medium for imparting knowledge. ‘This book is rather for 
reading and study than for the setting of many exercises in writing 
figures. It calls for oral expression far more than for written work ; 
but it is meant to call most for the quiet, studious effort of the child 
to think through the number-processes for himself in the light of 
the instruction of the teacher and of these pages. Many minds, 
of adults as well as of children, cannot at once comprehend principles 
and facts explained orally. We often need to see the printed words, 
and slowly and patiently to think out their truth and meaning for 
ourselves. We remember with more than twofold certainty what we 
have verified for ourselves after hearing from others. 

The value of numbers in real life is such as to warrant illustra- 
tions in the pages of text-books, both in topics, such as the clock, 
thermometer, calendar, and house address, and in pictures, which 
add to number the same interest they add to reading. Children 
are not alone in their frequent inability to realize in imagination 
a word-picture. Teachers are entirely justified in asking for their 
endeavor to awaken children to vigorous mental life the attraction of 
illustrations, and ought to seize every opportunity offered by arith- 
metic for training them to see, to image, to compare, and to represent 
the visible realities of the world. 


Author and publishers desire to acknowledge the valuable sugges- 
tions of Principal W. B. Gunnison, Ph.D., of Erasmus Hall High 
School, Brooklyn, N.Y., in reviewing the proofs of these pages. 


Wo BC: 


BLOOMFIELD, N.J., 
March 25, 1901. 


ai 2. | 


—_—  -_ 


SUGGESTIONS TO TEACHERS 


1. The preface explains the general purpose of the book. 

2. Read the book itself. The purposes of certain special features 
will appear only when seen in relation to other features. 

3. Do not hesitate to use in advance of the order in the book facts 
which appear later in these pages. 

4. While the purpose of number-study is to learn numbers, oral 
language expression needs to be encouraged. Develop the number- 
story features of early primary work as much as time permits. The 
speaking of English sentences tends to promote that rational under- 
standing of number-processes which is the end of Arithmetic as a 
science. 

5. See that the children do study this book, but do not ask them 
to study quietly over a quarter of an hour at any one time. Children 
tire quickly and recover even more quickly. 

6. Drill for the sake of instant accuracy; but do not follow any 
drill to the point of over-fatigue. Take great care not to drill upon 
things not essential. 

7. This book is only a collection of suggestions; it is not an en- 
eyclopedia of devices. Seek great variety in methods and devices. 
There are children who will not learn things in our ways. Try to 
find their ways of understanding number-facts and number-principles. 
Since historically our decimal system of counting by tens has grown 
from our having ten fingers, and since the authority of modern mathe- 
matical philosophy distinctly asserts the naturalness of counting upon 
the fingers, such counting should be permitted as a helpful stage in 
number-progress, but not to the extent of establishing a physical 
automatism. 

8. Every child has peculiar interests. Find them. For number- 
stories use facts which interest the various children. Remember that 
children have their “good” and their “bad” days. On their good 
days children sometimes learn an amazing amount of new matter. 

9. A boy or girl may be ready to undertake harder work than this 
book offers before knowing this book from cover to cover. Yet we 
should not forget that doing easy things over and over begets confi- 
dence, which supports us in our attacks upon new and harder problems. 

10. Neatness in writing tends to accuracy in all number-operations. 


od 


( 


LESSONS 


READING NUMBERS AT SIGHT 
Sizes, Forms, ANGLES 
Numsers 1 To 10, REVIEW 
READING NumBers, 10 To 100. 
FRACTIONS. 

Facts or NumsBers, 11 To 20 
Money 

DIVIDING AND MULTIPLYING AND PARTING 
TABLE OF Twos, AND HALVES 
TABLE OF THREES, AND THIRDS 
TELLING QUANTITIES 

Days OF THE WEEK 

RaTIos 

TABLE OF Fours, AND FourRTHS 
TELLING WEIGHTS 

NumBeERrs, 21-29, 30-99 
TELLING LENGTHS 

HunpREbDS, THOUSANDS 
ADDITION, SUBTRACTION 

House NuMBERS 


Fives anp Tens, Firras anp TENTHS 


SIxES AND TwELves, SrxTHs AND TWELFTHS. 


DATES AND CALENDAR 
TELLING TIME . 
TreLtinc HEAT anp CoLp 
Music Notes 


NuMBER TABLES AND TESTS 


96, 101-102, 105 


PAGES 

. 9, 60 

10, 20, 113 
fi 
15-18 
22-27, 86-87 
28-67 

, 81, 43, 98 
. 82-36, 56 
- 88-39, 45 
46-47 
48-49 
Ant 
66-69 
eye 
MET 
74-82 

91 


. 65, 85, 97 
108 
106-107 
108-109 
114-115 
116-119 
120-121 

. 122 
126-128 


HOW MANY ? 


TELLING NUMBERS AT SIGHT 


Number always means number of ones. 


; How many ones? @@@ How many ones ? 
ee Fay. me @ @ Find twos and 

How many twos‘ ® 

es J ee threes. 
AAG How many ones? Find five and one. 
eee How many threes? Look across. 

How many twos ? Look up and down. 
eeee low many twos? Find threes and two. 
@@@@ How many fours? Find five and three. 

How many threes? Find two fours and one. 

ee0@ ; eae 
eee Find six andthree. Find seven and two. 
@@@ Find five and four. Find eight and one. 
eceee@ ow many twos? e ms eo @ . e 
eeee@ 7 many fives ? 
2 How many fives ! ©eee 
| 
'@ @/\'|@6' & 
How eo. e600 ee 
many ? | @®@ e dnd x =< e ee 
J e@ 8 @8e @ 


Counting adds ones, or puts units together. 

Adding finds what new number tells all the ones in 
other numbers taken together. 

Subtracting takes a number from another number. 

Multiplying adds one number once or several times to 
itself. 

Dividing finds how many times a number contains 
another. 


9 


WHAT KIND? 10 
HOW MUCH? 


COMPARISONS 
/ Count these dots @ @ @ @ @ and crosses X X X. 
- We cannot add dots and crosses together because they are | 
not the same kind of ones or things. 
Count these circles O O O O andsquaresO OOOO. , 
Can we add circles and squares together? Why not? TS 


— 


Number always means number of ones of the same 
kind. 


This picture shows 
one inch square of 
I oleae Draw one EACH SIDE IS ONE 
square inch on paper. INCH LONG 


el 


But this picture shows 
two inches square of 
paper. Draw one square 
inch on paper, then on 
the blackboard. How 
many square inches do 
you find in this two- 
inch square picture ? 

When Mary would 
like two pieces of red 
paper, she should tell 
how large she wishes the 
pieces to be. 

Telling the size or amount or weight is called measuring. 

We find How many? by counting; and How much? 
by measuring. 


ov. 


11 STUDY 
ORAL 
* ALL FACTS OF 1 TO 10, IN REVIEW 
Additions : 
1+1=2 14+6= 7 24+38=5 24+8=10 38+7=10 
1+2=383 1+7= 8 24+4=6 8+38= 6 44+4= 8 
14+38=4 14+8= 9 24+5=7 384+4= 7 445= 9 
144=5 149=10 246=8 845= 8 4+46=10 
145=6 242= 4 24+7=9 384+6= 9 5+5=10 
Subtractions : 
10—9=1 9-8=1 8-6=2 [7-—4=38 9—3=2 
10—8=2 9-7=2 8-5=3 6-5=1 4—3=1 
10-—7=3 9-6=3 8-—4=4 6-4=2 4—2=2 
10—6=4 9-5=4 . 7T-6=1 6-—38=3 38—2=1 
10—5=5 8-—T=1 7—d=2 5-—4=1 2—l1=1 
Multiplications : 
Bete ee comb 2X de 8 Ko 10) ox a=9 
Divisions : 
10+5=2 8+4=2 9+3=3 6+3=2 4+2=2 
QUESTIONS 
1. How many are 545? 6. How many 3’s in 9? 
2. How many are 10—5? 7. How many are 8—4? 
3. How many 5’s in 10? 8. How many 4’s in 8? 
4. How many 2’s in 10? 9. How many are 247? 
5. How many are 9—6? 10. How many 3’s in 6? 


+ means and, 


— means less, x means times, 


9+3 means, How many 3’s are there in 9? 


4+, —, x, and + are called Signs. 


WRITING 12 
PRACTICE 


BLACKBOARD 


With thumb and fingers, hold the chalk crayon under the palm 
of the hand, and use free arm movements only. 
Blackboard figures should be three inches high. 


These figures are three inches high. 


» COMMA eed » PERIOD 


ONE INCH 
Se ee be ee ee eee 


0 1 2 3 
THREE INCHES 


Write on the blackboard five times with commas and 


Pe ic| Re2ee 3) ek evans Mama AEC! 


~ 


13 WRITING 
PRACTICE 


PAPER WITH PENCIL 


Write with a soft lead pencil. 


BOO 11640 


Pencil figures should be at least one half inch high like these. 


Each side of this square measures one half 
inch. We call this a half inch square. 


There are only ten signs for numbers, and each sign is written by 
itself. Most children, if asked to try, soon make figures both clear 
and beautiful. 


Mayrite |, 2, 3, U, 5, 6 1, & Gd, 0 
meric Od. |, 6, 5, U, 3, 2, 1. 
ere Oth (913 (15, Losi] 161g 
erent 20, 21,.22,23, 21 95,2621, 2890. 
5. Write 30, 31, 32,33, 34,35, 3b, 37,38 3d. 
6. Write UO,U/,U2,U3, UUU5,4b,U7,48,4q. 


SPELLING OF THE NUMBER-NAMES 


7 Lone. 92. two. -o, turee. 4four. 95, five. © 6.'six, 

8. T,seven. 8, eight. 9, nine. 10, ten. 0, cipher or zero. 

9. ll,eleven. 12,twelve. 13, thirteen. 14, fourteen. 
15, fifteen. 16, sixteen. 

10. 17, seventeen. 18, eighteen. 19, nineteen. 20, 
twenty. 30, thirty. 40, forty. 

11. 50, fifty. 60, sixty. 70, seventy. 80, eighty. 
90, ninety. 100, one hundred. 


ORAL 14 
TEACHING 


TEN, 10 


We always count by ones. We say that one and one 
are two, two and one are three, ten and one are eleven, 
twenty and one are twenty-one. If we would like to 
add three apples and two apples, we must know that we 
are counting three ones and two ones; we must know that 
three and one are four, four and one are five. 


eee-+trteeee~=>->-eeee e@ 
3 2 MYA GP wc 1) 


Until we reach the number ten, each number has one 
figure as its sign. ‘The sign of one is 1, of five is 5, of 
nine is 9. But when we reach the number ten, we find 
a number which has two figures as its sign. The sign of 
ten is 10. In this sign 10 are the figure 1 and the fig- 
ure 0, called zero. ‘This 0, or zero, with a figure before 
it at the left as we look at it, shows that the figure means 
ten times the number of ones for which it stands when 
it has no 0, or zero, before it. 


10 means 1 ten, 20 means 2 tens, 50 means 5 tens. 
yf 9 


e eee are | ten, ee oe ee ee are 2 tens, or 
ONO 195 OT Or LOS tell Woke ene On ae enO man Osu \vn Te 


All these dots together are 8 tens, or 30, thirty. 


Whenever a number has two figures, the figure to 
the left of the zero tells how many tens are meant. 


AGC aL eee Add 10 eeee eoe 
e + 


6 eee 6 @eee8 eee 


| 


sixteen 16 


15 ORAL TEACHING 
STUDY 


NUMBER-NAMES ABOVE TEN 


We call ten and one, eleven; ten and two, twelve. Most 
number-names for more than twelve things are names 
made of the single number-names from one to twelve. 
We call ten and three, thirteen, which is very much like 
three-ten. Four and ten are fourteen; five and ten, 
fifteen; six and ten, sixteen; seven and ten, seventeen ; 
eight and ten, eighteen; and nine and ten are nineteen. 


Read these numbers: 10, 11, 12, 18, 14, 15, 16, 17, 18, 19. 


@©eee# eee 0@2@080 @ 

e ie are ten. e ie ee are two tens. 
e@eeee @eeeoe @808280 @ 
Two fives we call ten. Two tens we call twenty. 


A great many years ago people called two tens, twain tens; then 
they used to call two twain. 

Twenty and one we call twenty-one; twenty and two, 
twenty-two; twenty and three, twenty-three; then we 
have twenty-four, twenty-five, twenty-six, twenty-seven, 
twenty-eight, and twenty-nine. 

Give the names for these numbers: 20, 21, 22, 23, 24, 
25, 26, 27, 28, 29. 

Read these numbers: 25, 24, 26, 28, 22, 27, 21, 29, 20. 

Three tens we call thirty. ‘Three tens and one we call 
thirty-one. Four tens we call forty. Fifty means five 
tens. Sixty, six tens. Seventy, seven tens. Kighty, 
eight tens. Ninety means nine tens. 

We have another name for ten tens, one hundred. 


10 ten 16 sixteen 30 thirty 90 ninety 
lleleven 17seventeen 40 forty 90 +1= 91 

12 twelve 18 eighteen 50 fifty 90 ++ 3 = 93 

13 thirteen 19 nineteen 60 sixty 90 +5 = 95 

14 fourteen 20 twenty 70 seventy 90+ 8= 98 

15 fifteen 21 twenty-one 80 eighty 100 one hundred 


READING 16 
WRITING 


COUNTING 


: sae ot ere 
Count by twos, beginning at 2. 


2 + 6 Br SheeO ci. tL 2ae ea LO ames 20 
BP) UDA) QOV (2B SU) 9-320 parte anes ne 40 
BF, AL: 946): 4B OO) 8b2e sate hob ee 60 
Bee GG4 yi 60°: OBR 0°) Tizai aid tee wes 80 
62984: 86) 1884-90. 9270 Os) §O6" Sos eee 


These are called the even numbers. 2 divides each 
number without a one left. 
Count backwards, beginning at 100. 


Count by twos, beginning at 1. = 


1 3 5) T cel dn] OS 99) 1 See 19 
Ble 23-225) 7 2 295 eh eae eed eee 39 
Al} AS. 450° AD SON Ole, (0375 dary aoe 59 
Bie 6o: ~ + Oo 00 et OO eT Lai Fo gee ee 79 
Bo) 8S yhoo Ly ASO) weele, 905 Sao 99 


These. are called the odd numbers. 2 divides no num- 
ber evenly. One is always left over. 
Count backwards, beginning at 99. 


Count by threes, beginning at 3: then backwards. 
BY 6. (Qo), 12) Loe BLS peel eee, oe 
386 39 42 45 48 S51 54 ST 60 638 #42466 
12) 1) 7°18 Sde sh84 2 87,190) 195 eee 


5 10 °° 15 20 925) 30 35) 40 ae 
5d 60.1 .65.-_.10 © 1x 80'S SS ee OOls as ere 
Count by sevens, beginning at 7: then backwards. 
7 14 21 28 35 42 49... a 
56 63 70 TT 84 91 98 


17 COUNTING 


THINGS TO DO 


1. Count all the boys in the room, giving them odd 
numbers, and all the girls, giving them even numbers. 
How many are there in all? Can each boy and girl 
remember the number given to him or to her? 


2. Cut out about thirty squares of paper. Write the 
numbers to thirty, one number on each square. 


3. Cut each square into two pieces, and using the 
vther side of the paper, number each of the pieces. 


4. Draw lines like these, 
but longer, so as to make 
more squares, and number 
each of the squares. Cut 
_ the squares apart. 


5. Count the number of 
panes of glass in all the window sashes of the classroom. 


6. Count the number of desks in the room, and then 
the number of chairs. Write each number for the desks 
upon a piece of paper, and place it on the desk to which it 
belongs. : 

7. Count marbles, shoes, hands, fingers, hats, caps, 


pencils, splints, blocks, and other objects, as far as one 
hundred. 


8. Read the numbers of the pages of this book as far 
as one hundred. ) 


9. Count the number of lines of print upon this page. 
10. Write the number of the house where you live. 


11. How many chickens, or sparrows, or ducks, or cows, 
or horses, did you ever count together at one time ? 


WRITING Sri 


PRACTICE 


6. 


NUMBER TABLE 
mann CMH. 1p ames ete) 19) 
Dh 19. DD SOMO! 5 Db Oe cece 
(3? 238 Ses 5B Sree ae eda 
Paola Bree Mb RMS MED oy WE PLE ck 1) 8 
PeyeMonsi an Ulayiotsieor fs. wo ci 
Ib 2636 Ub5bbb7b &b Gb 
F129 37) 4] SiOet See Sale 
16 2838 US 58 bE 18 FE G8 
Id 2434 44596414 8q qq 
[0 20°30 05.050 | 06/6 ad Onnore 


Write ten, eleven, twelve, thirteen, fourteen, fifteen. 


BO OV la Ome eae GU 


Write sixteen, seventeen, eighteen, nineteen, twenty. 
Write twenty-one, twenty-two, twenty-three, twenty-four. 
21 22 23 24 
Write twenty-five, twenty-six, twenty-seven, twenty-eight. 
25 26 27 28 
Write twenty-nine, thirty, forty, fifty, sixty, seventy. 
29 30 40 50 60 70 
Write eighty, ninety, one hundred, one hundred one. 
80 90 100 e GLOd 


19 BUSY 
WORK 


THINGS TO DO 


We can use instead of dots: 


eececee5aeeee 
Deere et ee. Se circles like this O, or 
eceoeoeveaeee0e crosses like this x, or 
Barer ne: 22. @ 6.0 © signs like this +, or 
@®eeeee?3d?s8 ee . : R 

triangles like this A, or 
eeeeeeee?ees © 5 : ] 
wate e@e6eee¢e squares like this UO, or 
eee oer, © © any forms, such as these, — 
@eeeeee?e?e? ee 
@ee7eee%ees8es ee 


OHRVOG 


1. Make 100 dots on paper or on blackboard. 
2. Number these dots or squares 1, .2, 3, etc., like 
this e or this [. 
1 l 


3. Make lines around every 2 dots like this, @ e) 


4. Make lines around every 3 dots, G3) or @ +) 


5. Make lines around every 4 dots, every 5 dots, 
every 6 dots, every 7 dots, every 8 dots, every 9 dots. 
6. Connect every dot with all the dots next to it, like 


this, — 


7. Use red chalk or pencil and mark every alternate 
dot which has an even number, like this @ or this @). 

8. Use blue chalk or pencil and mark every alternate 
dot which has an odd number, like this e or this @). 

9. Mark with blue, or yellow, or red chalk every third, 
every fourth, every fifth, every sixth dot, ete. 


Use new sets of e, or (, or + tables except for 1 and 2. 


DRAWING 20 


FORM 


With a stick, or a splint, or a pencil, we can rep- 


resent a line across, or}| up and down, or 


slanting up to the right, or down to 
the right. With two ea pero we can make 


& CTOSS ora T or an angle like this 


sticks we can make a form 
like this It is called a triangle 
because it oN has three angles. 

With four sticks each of the same length, we can make 
squares like this If we have a pair of sticks of 
the same length, ae and another pair of sticks longer 


than the others, 


three 


or P| or this Try and see. With 


two like: these ean 


two like these ———————==,, we can make a_-rectangle 


like this If we draw a line through our 
rectangle eee to opposite 
corners, we have two 


triangles inside the rectangle. If we 
have the longer sides twice as long as 
the shorter sides, then inside our rec- 


tangle we have two squares. 


AAT ORAL TEACHING 
STUDY 


PARTS OF FORMS 


How many little 
squares do you find 
in this large square? 

This square is two 
inches wide and two 
inches high. 

‘ When things are 
exactly like each 
other in size, we call 
them equal. If you 
find inside of the 
square A four squares 
each of the same size, 

then all four parts of A are equal parts. 


MEASURE MARKED IN INCHES 


Is this square as large as the square 
marked A? Is it as large as any 
part of A square ? 

Measure this square B, using a ruler 
marked with inches; cut a square out 
of paper of the same size as B, and 
: see how many little squares as large 
as B you find in A square. 

If you find that square A is four times as large as the 
square marked #, then it is right to say that B is one 
fourth as large as A. 

If A is four times B, then BP is one fourth of A. 

If A is 4 x B, then B is } of A. 


ORAL TEACHING 99 
STUDY 


EQUAL PARTS OR FRACTIONS 


A number is always a number of ones of the same kind. 
A fraction is always one or more of the equal parts of 
some one thing. 


eC Co Ee 


Here are four forms, A, B, C, and D. 

Each is of a different size from the others. 

A is divided into five parts. Bis divided into four parts. 

Cis divided into two parts. JD is not divided. 

Each part of A, each part of B, and each part of C is 
the exact size of D. 

There are 5 D’s in A. Count and see. 

There are 4 D’s in B, and 2 D’s in C. 

Each part of A is equal to every other part. The five 
parts are equal. 

Each part of B is equal to every other part. The four 
parts are equal. 

One part of Cis equal to the other part. 


We ¢all equal parts fractions. 

Each part of A is a fraction of A. There are five parts. 
Each part of A is one part of A. We print this, 4. 
The 1 above the 5 means that we are taking one part. 
The 5 means that there are five equal parts in A. 

Each part of B is a fraction of B. There are four parts. 
Each part of B is one fourth of 6. We print this, 4. 
The 1 above the 4 means that we are taking one part. 
The 4 means that there are four equal parts in B. 

Each part of Cis a fraction of C. There are two parts. 
Each part of Cis one half of C. We print this, 4. 


23 ORAL 
WRITTEN 


REVIEW 


Can you tell what number separates the numbers in 


these 
abs 


10. 


questions, 1 to 9, below ? 
Bote 14. re eae 7, 10-20-3040; 
p—Ve1G—1 7; Beli, ere 


. 8-12-16-20.. 6. 10-17-24-31. 9. 5-13-21-29. 


Write on the blackboard five times without commas 


and period : 


aL. 


nbs Ee 


BS voMyeSnsO: 4S" 5 U3) O | 


Write on the blackboard five times these numbers: 


10, 12, 28, 34, 45, 5b, by, 18, 89, 90. 


12. 


35, 


Write on the blackboard five times these numbers: 


Db, 579, 680, 258, 813, 4490, 


__. SE 


The rectangle is not divided into equal parts. 


The rectangle is divided into two equal parts. 
Each part is one half the whole rectangle. 


_ ae ee 


The rectangle is now divided into three equal parts. 
Each part is one third the whole rectangle. 

O is 3, one half, of M, for there are 2 O's in M. 

Sis 4, one third, of M. Why? 


ORAL TEACHING 94 
STUDY 


PARTS OF NUMBERS 
What part of A is a? B= a, 
[ie] B is one half of A. A equals 2 B’s. 
A B jf ee 


») 


fod 


falala| What part of Cisa? C=3 B’s. 


B is one third of C. a= of C. 


C 
ke How many dots do you find in B? 
How many dots do you find in A? 
A B 
4=2x2. 4 are twice two. 
ale 2=40f4. One half of four 1s 


C two. 


b= 24 x) 08) OW erlind Ber ees 


r= . <3 Oe, e @ 2 
Z=— 1 01 6. One third Of Six 18 Uw0-. | @2e 6.6 esetnes 


hese are pictures of the two fractions B 
4 and #. We call the picture-fractions 4, 
one half, when we 


think that A=2 B's. 
pe |e! poe Then B is only $ of 
| | A. 
pele ie} We call the pic- 
A B ture-fractions 2, two Be ee 
fourths, when we 


think that A’s 4 dots = 2x B’s 2 dots. 
Bs 2 of A. 4 is the same amount ot 


value as 4, A 


25 ORAL TEACHING 
STUDY 


PARTS 


Cut out of paper a square one inch on each side. 

Then cut out a rectangle two inches long, one inch high. 

The square is one half as large as the rectangle. 

Cut the square into two equal parts, one inch by 3 inch. 

Cut the rectangle into four equal parts. 

Do you see that the 2 parts of the square are ? of the 
rectangle ? 


There are 5 equal parts in A. falo]elale| 
Each is } of A. 
A 


a+ 6=2 fractions of A = 2 of A. 
a+b6+c= 8 fractions of A = 3 of A. 
a+6b+e+d=4 fractions of A= 4 ol A. 


a+b+e+d+e=5 fractions of A = 32 of A. 


But as there are only 5 parts in A, 3 of A =all of A 
Peel cA. 


A This form-picture is divided into two 
parts, b+¢e. b=tof A. c=4 of A. 
Leal The picture of 6 is divided into three 
parts, d,e,f. d=}ofb. e=} of b. 
P ; f= of b. 
If we divide ¢ into three parts, then A will have 6 parts. 
If A has 6 parts, then d=} of A. 
d= of 4 of A, because d is $ of 4, which is 4 of A. 


9 . 
2 4+dthtd=? 9 dthe? 
1 i aay Ye ey 
Sane ac ia ome 


Cut and fold pieces of paper to show the answers to 
these six questions. 


ORAL TEACHING 26 
STUDY 
PARTS OF NUMBERS 
5 names 5 |’s 5=I|1111 1=+} of 
3 names 3 |’s 3= Ill 1=4 of 
4 names 4 |’s 4 = | 1=} of 
2 names 2 Is 2= |] 2=1 of 2 
When we say one fifth of anything, we mean that the 


thing is divided into fifth parts, into five equal parts, and 
that we are talking about one of these parts. 

When we say one fifth of any number, we mean that the 
number is divided into fifth parts, into five equal parts, 
and that we are talking about one of these parts. 


Here is a picture i . There are 2 rows up and down 
of the number ten ee of 5dotseach. The 10 is divided 
seen in dots. * © into 2 equal parts of 5 each. 

e@¢ 

There are also 5 rows across of 2 dots each. The 10 
dots are divided into 5 equal parts of 2 dots each. 

We can say that e e are $-®—— of 10 dots, or +. 

Zidotes ao eat.* 
2x — 10 2=10+5 2 is ¢ of 10 2= 10 
ee 

We can say that $e° are *® of 10 

Ye Can Say 1at ee are 10 O . 
Dix 210 5=10+2 5 is 3 of 10 5= 10 

Ve Adde8 Atl) CO A ine ieee es 

2 ee 1 (14 SS 6 ae 

2. Added : Bo A) ee Ae oes 

V4.2. 8 (27 ORS 0 ee 


27 COMPARE 
STUDY 


PARTS OF NUMBERS 


Sometimes we take things apart. We split a piece of 
wood into separate pieces; we cut an apple in two; we 
spend a quarter of a dollar, which is a part of a dollar. . 

When we make two equal parts of anything, we call 
each part one half. The figures for one half are . 

When we make three equal parts, we call each part one 
third: 4. Each part of four equal parts is one Sess or 
one quarter: }. After these we have one fifth: 4. 


A igun Maaeed erarrkee 
or ec A: 
B has 2 A’s. 


D 


A Measure these lines 
C has 3 A’s. A and see if these stories 
D has 5 A’s. A are true. 


We can take parts of form-pictures. & in Ee 
We can take parts of number-pic- aS] 
in 
tures. 


We can take parts of numbers. 


I 
Ct CO|t bo] 
wah 


in 4 


bo @ @ 


We can tell parts by figures. 


When the parts of anything are equal to each other, 
then we call the equal parts fractions. 
There are ten onesin ten. There are three ones in three. 


eas pele [2 Lote], ee a 
tenths of the 


whole figure is } inch long, how long are =; of it ? 


Three are three tenths of ten. 3= to of 10 


ORAL TEACHING 98 
ANSWER 


ELEVEN, 11 


If we have ten things and add one thing to them, the 
name of the number of all these things together is eleven. 


ee @0@ 
0C000000000+0 
Morph 6 6.7 8 Blow T ae ne cae 4 
10 + 1 are eleven. Ten and one are eleven. 11 


We write eleven with the figure 1 twice: 11. 
In the figures 11 for eleven, the unit one, 1, has the 
place of the zero, 0, in the figures 1 and 0, printed 


like this: 10, for the number ten. : 

In the number eleven, printed as 11, the second < 

1 shows that the first 1 stands not for one, 1, unit, e 

but for one ten, or 10. 11 means 1 ten and 1 unit, ; 

like this group of dots: zi 
@ @ 


8+3=11 7+4=11 6+5=11 11—5=6 

1041=11 94141=11 54541=11 24+384541=11 

11—1=10 11—2= 9 94+2=I11 7+2+4+2=11 
With splints and counters, show each of the above facts. 


1. John had five cents and Tom had six cents. How 
many cents did they have together ? 

2. There were ten boys; one of them had two cents, 
nine of them had each one cent. How many cents did 
they have together? 

3. Mary had eleven cents. She spent four for apples 
at one cent each. How many cents were left? 

4. ‘Tell number-stories about cents, using these number- 
facts: | 11e— 1515 2 LOS 9 te a eee 

5, Add shloms (00.0 sie ea sibtractege Lelie deen 


99 ORAL 


MEANING OF SIGNS 


The sign of multiplication is x; it means times. 
The sign of division is +; it means divided by. 

? asks a question. It is called the question mark. 
When we ask 10 + 1 = ?, what does the + mean ? 
What is the answer to 10 +2=? 


What does this. mean? What is its name? 


1 

4 

3 

4. What is the name of this mark ,? 

5. What does this mark + mean? And this —? 

6. Read these questions in words: 

83x3=? I11=8.x? and how many over? 6+5=? 


ieee 68-711? «61142? 848 424-14+7=11. 


ELEVEN 


7. Is eleven an odd or an even number? Why? 
What is the next number after 10? before 10? 


. 
. 


How many more are 11 than 10 things ? 


10. George had eleven marbles and Charlie had 8. 
Which had more than the other? How many more did 
he have ? | 

11. Take 11-splints. Make 2 squares with them and 
one triangle. 

12. How many triangles can you make with eleven 
splints? How many splints are left over ? 


a QS Se SSE es ier ae am at 
en ES oy Teed a A GD. ig ao 


14. Can you remember several numbers when written 
on the board and then quickly erased? ‘Try and see. 


ORAL TEACHING - 30 
ANSWER 


TWELVE, 12 


If we have ten things and add two things to them, 
the name of the number of all these things together is 
twelve. 

+. ee @ @ e 

2999999999199 coc ces tie 10 

2 

10 + 2 are twelve. Ten and two 12 

are twelve. 


We write twelve with the figures 1 and 2: 12. 

In the figures 12 for twelve, the unit two or figure 2 
has the place of the zero, 0, in the figures 10, for the 
number ten. In the number twelve, printed as 12, 
the figure 2 shows that the figure 1 stands not for 
one unit, but for one ten or 10. 


12 means 1 ten and 2 units, like this group of dots: 


In the numbers eleven and twelve, printed 11 and 
12, we say that the 1 in each number where it is 
the first figure, reading from left to right, is in tens’ 
place and that the second figure in each number is in units’ 
place. 


12 things make one dozen. 


When we say, “ Mary’s mother who keeps hens sent 


b] 


Mary with a dozen eggs to sell to the grocer,” we mean 
that Mary carried twelve eggs. 
10+2=12 9+3=12 8+ 4=12 T7+5=12 
!-—6= 6 12= (=o) 12-10] 29 12 ee 
Show each of these facts with counters and dots. 
1. Tell number-stories about cents, or eggs, or marbles. 


2. Mary has seven dozen eggs and Susan has five dozen. 
How many dozen have they together ? 


a ee 


1 copper penny is worth 1 cent. 


31 


PENNIES, NICKELS, 


ORAL 
WRITTEN 


AND DIMES 
The sign, | ¢ 


1 nickel is worth 5 cents. We can write nickel, 5¢ 


1 dime is worth 10 cents. We can write dime, lot 


1. Grace bought half a dozen of cookies at 1¢ apiece. 
She gave the baker a dime. What change did he give 
her ? 

2. I paid a nickel for half a dozen pens. 
cents would a dozen pens have cost ? 


How many 


3. 10 pennies are worth 1 dime. 2 nickels are 
worth 1 dime. Why? 
4. Which would you rather have, a dozen pennies or a 


dime ? 


Why? 


5. It usually cost# 5¢ for a man to ride on the street 
cars, and 3 cents for a boy. How many men can ride for 
a dime? How many boys ean ride for a dozen pennies ? 

6. Did you ever see a pile of a dozen pennies ? 


7. Write on the blackboard a story about pennies, 
nickels, and dimes. 


OTHER NUMBERS 


2+7=? 5+3=? 6+2=—? 7—4=? 3+6=? 
3+7=? (—o=? 9—4—" 9—6=? 10—9=? 
(+3=? 9—2=—? 14+9=? 9—1—? (1+2=? 
6+4+4=—? 10—3=? 444—' (—4=? 8—6=? 
94+1—? 10—4=—? 4—3= §+5=? 10—2=? 
9—5=—? 10—5=? 4—6=? 10—8=? 24-8=? 
10—1=? 84+2=? 1+1=? re a 5—2=? 


STUDY 39 
ANSWER : 


DIVIDING AND MULTIPLYING 
12=—6+46 be? = 12 1232 3.6 


Add 6 Subtract 12 
6 6 
How many are4+4+4? 8x4=? 
How many are 3+3+4+3843? 4x3=? 
In 1 above how many 4’s do you count ? 
In 2 above how many 3’s do you count ? 
Show 1 and 2 by splints, counters, pennies, or dots. 
Is it true that 8 x 4=12 and 4 x 83=12? 

When we find how many fours there are in twelve, we 
count 4’s until we reach 12. 4+4are 8. 844 are 19. 
There are three fours in twelve. Multiplying, or finding 
one number times another, is rapidly adding one number 
to itself. Dividing, or finding how many times one num- 
ber contains another, is rapidly taking away the same 
number several times from another number. 


12—-4=83. We find three fours in twelve. 


er 


NUMBER-STORIES 


7. Charlie had twelve apples; and when four boys 
came to see him, he wanted to give each of them the 
same number. How many could he give to each? 

8. There were two boys who had six marbles each. 
How many did they have together ? 

9. Lulu had an afternoon tea-party. Her mother gave 
her a dozen tea-biscuits. She and Clara and Mabel ate 
them all; each ate as many as the others. How many 
did each eat ? 


89 STUDY 
ANSWER 


MULTIPLYING AND DIVIDING 


ask 5x2=?, what does the x mean? 


And what does the ? mean? 


1. When we 
And what does the = mean ? 
2. What is the answer to 5 x 2=? 
1+1=2; or there are two l’s in 2; 
orl x2=2; or 2x1=2 
3. 1+1+1=8; or there are three 1’s in 8; 
orl x $= 8s or 38 x 1= 3: 
4. — is the dash or blank mark. Can you fill in the 
words or numbers that are left out as shown by the dashes ? 


In 5 there are 


4 apples at 1 ¢ apiece will cost — cents. 
In 6 there : 
In 7 there are — 1’s; or 7x 1=—. 


5 1+1+1+1=4; or four l’s=4; or there are four 
1l’s in 4; or 4 times 1 are 4; or4x1=4. 


94+2+4+24+2=8: or 4 2’s=8:; or there are four 2’s 


in &. 

Bee eas 2x5=? Dea b+-2=7 
6+3=? 8+4=—? AM Zee Dor aat 
10+2=? 10=5x? 8=2x? aX t=30 
9+3=? 9+5=?+? T+38=?+? 6+8=? 
12+3=? 12+5=?4+? 12+4=? 11+-3=?+? 


A dozen cents less a dime = how many cents? 


7, 1+1+1= 83; or three l’s=3;3 or 8x1=83. 
2+2+2=6; or three 2’s=6; or 3x 2=6. 
8+3+3=9; or three 3’s=9; or 3x 3=9. 


WRITTEN 34 


REVIEW 


1. Subtract: 5 fp 9 eg ake | ake Hae) 
eh 5 6 ea 

2. subtract : 10 8 10 T 8 10 9 6 
Bais lente fr 

2) pubdiuracue LU 9 T 4 6 8 6 8 
SOTO WEES OD Se 

4: Add: 5 6 2 Se ol. 25. Subtract. Zeal ela 
rf 6 10 3 11 V Gas Pap 3 Gu aL 


6. Copy and answer: 
S—7=) lO 6-e) MOS ae? + ee 6—?=2 
o+?=10 10=7+4+? 10=44+? 10—T=? - 10—2=? 
F842? 2.447210) 93-47-10) 984 "= 10" eee 
ee UO oe 10—?=7 10-—?=4 2-—?=5 
7+?=10 9-—?=4 o—?=2 6=?+4 10—?=4 
Write in words your answers to these next two ques- 
tions: 
7. Two boys had 5 pennies each. Another boy had 2 


pennies. If they had put them all together, and had then 
divided them equally, how many would each have had? 


8. They did not do this, but when still another boy 
joined them, they bought for one cent apiece as many 
doughnuts at the bakery as they had cents, and divided 
the brown doughnuts equally, as many to one as to an- 
other. How many doughnuts did each have ? 


9. Tell stories about 12 — 6,6+6,44+4+4, and 6 x 2. 


35 STUDY 
ANSWER 


DIVIDING 
Often we write division-questions in this way 3 lO 


This means just the same as 10 + 2=5. 5 
We may read 9 )| QO either 10 divided by 2 are how 


many ? or how many 2’s are there in 10? 
@eeee 
@eee?e 
may think of them as divided into 5 x 2 dots or 10 dots + 5 

e | e | @ | @ | ® 
@'e/e@|e@/@ 


Here are ten dots We can show that we 


by drawing lines between every 2 dots or as 


divided into 2 x 5 dots or 10 dots +2 by drawing a line 
oD 


between every 5 dots 
©9ee8s @ 


Dividing is the opposite of multiplying. 
Dividing is taking numbers apart; multiplying is put- 
ting numbers together. 


SOMETHING TO DO 


1. Take 12 splints or counters. Separate them into 
one bunch of 6 and another bunch of 6. This is dividing 
12 splints by 2. How would you divide 12 splints by 6? 

2. Take the 2 bunches, each of 6 splints, and put them 
together. This is multiplying 6 splints by 2. What 
would you do to multiply 2 splints by 6? 

pele oe Ie 8 KAS Ax BS 

Answer these questions by dots or counters. 

4. 2)4 2)6 2)8 2)10 2)12 3)6 3)9 3)12 
mS 4)12 

5. A grocer sold half a bushel of onions. What part 
of the bushel did he have left ? 

6. One half of 6 splints = how many splints ? 


STUDY 36 
ORAL 


DIVIDING WITH A NUMBER OVER 


1, Find3’sin?. 2x38=6 641=7 7+3=(8x2)+1. 
7 divided by 8 are 2 and 1 over. 

2. Find 4’s*in 11.92 x 4] 8) “Sse oe eae 
= (4 x 2) ta 3. 

3. How much is 12+5? 12 divided by 5 are 2 and 2 
over. 


4. 5)1l. Five is found in 11 twice and 1 over. 
5)11 41. 


5. T)12 "T1246 ‘6. 8)10' 29 49 do ee 
7. 12+10=? 8+5=? 9+8=? 124+9=? 


When you see these marks (_ ), called parenthesis 
marks, around numbers, they mean that we must do first 
what the sign inside says: (8 x 2)+2=? means 8 x 2, 
which are 6, then add 2=? The answer is 8. But the 
answer to 8 x (2+ 2) is8 x 4=12. 


REVIEW 


s. If I owe you 4%, and give you a dime, how many 
cents must you give me back? 


9. A piece of ice weighed 10 pounds in the morning. 
In the evening it weighed 2 pounds less. What was its 
weight in the evening ? 

10. Harry bought a bottle of ink for 3 ¥, a pencil for 1¥. 
He gave the clerk a nickel. Should the clerk give him 
any change ? 

11. Make a story about 3 and 4; about 2 and 5; about 
6less1; about3andland2; about 12 +6; about ll +5; 
10 + 4. 


37 ORAL 


QUESTIONS 


1. How many two-cent stamps. can we buy for a dime? 
How many can we buy for a dozen pennies ? 


2. Frank is 10 years old. His brother is 4 years 
younger. How old is his brother ? 


3. Edgar has a dime. Willie has a nickel and 3. 
How many more cents has Edgar than Willie ? 


4. George earned a nickel on Saturday forenoon and 
another nickel in the afternoon. On Saturday evening 
he spent 6%. How many cents had he left ? 


5. A post was 10 feet high. 2 feet of it were in the 
ground. How many feet were above the ground? If 
Tom is 4 feet tall, how much higher is the post ? 


6. I buy an orange for 3¢ and hand the fruit-dealer a 
dime. What change should he give me ? 


7. There were 10 plum treesinan orchard. 2 of them 
died. How many lived? How many more would the 
farmer need to plant so as to have a dozen in all? 

8s. Arthur gave a dime for a flag and atop. The top 
cost 4¢. How much did the flag cost ? 

9. George gave 3 apples to each of 4 boys. How many 
did he give in all? 

10. Alice had 10 pansies. She gave away 3 of them. 
How many had she left? If she divided the number left 
among three friends, giving each two, would she then 
have any pansies for herself ? 

11. Her father gave Helen a dime. She bought 5¢ 
worth of braid. How many cents had she left ? 

12. Louis spelled 3 words and James spelled 4. How 
many words did both boys spell ? 


STUDY 38 
ANSWER 


TWOS 
13, 12% Bly dy WO RGy ih SH BONE LO miilentes 
13 14 15 1617 18 19 20 21 22: 93 94 
+2=2 6+2= 8 12 2 14 18 + 2= 20 
+9=4 §+2=10 144+ 2=16 20 +2= 2? 
as 2B NG oes Te 16°029'= 18 9949-94 


2x1l= 2 2x%.T=14 
ees ol Pepa ths 
eee 2x 9=18 
ge 4s 2x10 = 20 
2x5=10 2x 11=22 
eG eb) 2x 12=94 


MULTIPLICATION TABLE OF Twos 

We read it either this way, 2 2’s are 4, or two times two 
are four; two 3’s are 6, or two times three are six; and 
so on. 
6-+6— 12. two 6’si= sixiQ’s; ) 2422-6 Qe Do aa 

10 + 10 = 20 two 10’s = ten 2’s 
24+24242424242424242=20 

1. Copy the Table of Twos on paper. 

2. Count by 2’s to 24. Write this counting. 

3. Show that two 5’s are 10, two 9’s are 18, two 12’s 
are 24. 

4. Show that two 4’s are 8, two T’s are 14, two 11’s 
are 22. 


—E———e 


——EOe 


-< 
4 


39 STUDY 
ANSWER 


HALVES 


When anything is divided into two equal parts, each 
part is called a half. ‘Two halves make a whole. 


BAN 


tectangle in halves Circle in halves Triangle in halves Square in halves 


When anything is divided into two equal parts, the 
parts are called halves. 

Draw a line 2 inches long. Divide it into halves. 

Draw a square. Divide it into halves. 


One half is written 4 in figures. 


1. How many halves are there in one dollar? 


2. How many halves are there ina pie? If a pie cost 
10 cents, how much will half a pie cost ? 


3. James had one dollar. He spent half a dollar for a 
ball. How much money had he left? 


4. If you bought a cookie and ate half of it, how much 
of it would be left? Would the part of it left be equal 
to the part you ate ? 


5. One orange is what part of two oranges ? 
6. One basket is what part of two baskets ? 
7. One half of two cents is how much ? 

8. One half of four cents is how many cents ? 


9. George earned ten cents by doing errands. He 
gave half of the money to his sister. How many cents 
did he give to her? 


10. 4 of 10 cents is how many cents ? 


bole 


ORAL TEACHING 40 
STUDY 


THIRTEEN, 18 


When we have ten things and add three things to them, 
the name of the number of all these things together is 


thirteen. 10 
(2) 
e©e2ee¢ e o 

Php cee ane G Om eaeereysstcs saa | 

10 + 3 are thirteen. Ten and three are thirteen. : 

] 


We write thirteen with the figures 1 and 3,13. ° 
We put 1 in tens’ place, and 3 in units’ place. 
13 means 1 ten and 3 units, like these dots : 

12 +1=13. <A dozen and one are thirteen. 

Thirteen is the first name of a number which is 
made up with the thought of ten as one part of 
the name. All names of numbers above thirteen as high 
as ninety-nine have at least a t in them to make us 
remember ten. 

Show by splints that each of these number-facts is true: 
114+2=18, 18-—4=9, 13—6=7, 84+5=138, 13—10=3. 

1. When your fathers and mothers were little boys and 
girls, thirteen was called the “ baker’s dozen,” because the 
bakers gave them not twelve but thirteen biscuits or rolls 
when asked for a dozen. How many more did they give 
than the bakers give now for a dozen ? 


2. A hen sat for three weeks on thirteen eggs and 
eleven little chickens came out of their shells one day. The 
day after the other eggs had little chickens peep out. How 
many chickens came out of their shells the second day ? 


3. Tell number-stories about these facts: 10+ 3, 13—5, 

et oO are i se Lene cl eee 
4. Add312 11°9 6.5, 5) Subtracteel3vl3eioelomis 
1- 24.7.8 Diy 4 Gees 


—_——_—  — ee 


4] 


Peo 1s 


1. One half is a fraction. 


This | is 2 times thissees 2 


INCH 


ORAL 
ANSWER 


| 


HALF INCH 


A fraction is one or more of the equal parts of a thing. 


2. 


of 4¢=? 
of 12¢=? 
of 10=? 


Di DOR DR DO 


| ea 


| — <O bo 
| — 4 bo 


|r w& oO 
lr wan 


4 of 4=? 4 
eect oces2 1 
4 of 6=? 4 
Gr Gg 27 en ts 
C2 2210-7" 10— T=? 
11-—38=? 6+ ?=10 
iss sp eaiteb se 110 
AOE 10h A=? 
1097) -2)18 8) 18 
4 3 i 8 
1 DB 5 1 
1 2 fe 1 
3 5 y 6 
-4 3 2 5 
Je 1 Z 1 
a 3 1 7 
‘a, 3 1 2 
1 3 ui 1 


of 9=?+4? 
oF lL ?+? 
of 2=? 
of 8¢=? 
9+3=? 
6+ ?=138 
10+1=? 
{ee ay ey, 
O= haap ey 
12+10=? 
2 4 6 
2 3 2 
3 4 5 
A 3 4 
2 9 4 
3 1 5 
1 2 4 
6 s 1 
1 1 4 


What is 4 of 2, of 4, of 6, OL Srob 10 cof 127 


ORAL TEACHING 42 
ANSWER 


FOURTEEN, 14 


If we have ten things and add four things to them, the 
name of the number of all these things together is fourteen. 


©000000000+0000 vonnrenciare 10 
ao % ee ee ce 4 
104+4=14. Ten and four are fourteen. 14 
We write fourteen with the figures 1 and 4, 14. $ 
We put the 1 in tens’ place by setting the 3 in : 
units’ place. 14 means 1 ten and 4 units, hke this’ e 

group of dots: ates 
© 

B4l=144° 1279514 oe 

@eo 


A dozen and two are fourteen. 

Of what does the syllable “teen” in fourteen remind us ? 

Show by splnts that each of these number-facts is true: 
114+38=14, 9+5=14, 8+6= 14, 7+7=14, 
[{—2'= 12. 

NUMBER-STORIES 

1. Tom was fourteen years old. His brother was six 
years old. How many years older was Tom ? 

2. Mary was seven years old, and Susan was seven, too. 
How many years had both lived ? 


3. Wilhe and his little brother had together fourteen 
pennies. Willie took eight pennies for himself and gave 
George the rest. How many did George have ? 

4. Tell number-stories about these number-facts: 14—8, 
7+7, 14-4, 945, 1242, 138-1. 

S 14-722 142-2275 7K%2=14 2x74 

Show each of these facts by splints and counters. 


43 ORAL TEACHING 
ANSWER 


FIFTEEN, 15 
When we have ten things and add five to them, the 
name of the number of all of these together is fifteen. 


GO.O.01OLO O10:Oi OO O:'0. 0 © wan setae, 
» ° eevee 


We write fifteen with the figures 1 and 5, 15. 
We put the 1 in the tens’ place by setting the 5 in 
the units’ place. 44 

10+46=15. ~o Ten and five are fifteen. 

15 
1384+2=15 9+6=15 12+38=15 

Show by splints that each of these number-facts is true: 
144+1= 15, 11+4= 15, 8+7=15, 15—5=10, 
15—7=8, 15—9=6 


~ 
@@eeeoeeeede @ 


MONEY 
5 cents =1 nickel. 
10 cents =1-dime. 


2? nickels = 1 dime. 
1 dime and 1 nickel make 15 cents. 38 nickels =15 cents. 


1. Three boys had three nickels. How many pennies 
or cents could they get for these nickels all together ? 

2. Willie had 6 pennies, Johnny 5, and Charhe enough 
more to make 15 pennies. How many did Charlie have ? 

3. Mary’s father gave her fifteen cents. She spent one 
nickel for a little china doll, and four cents for a picture 
card to put in her doll-house. How many cents were 
left ? 

4. Louise had a dime, and Sarah a nickel. They spent 
six cents for ear fares, and five cents for cookies. How 
many pennies did they have then ? 


WRITTEN 4A 


REVIEW 


1. Addi:.11..10 120987. 2Subtract:.147 14a 
9 A ae) 5s La Gael 


3.15+8=5 5x8=15 Answerld+5= 38x5= 
4. Show each of these facts by splints and counters. 


5, Add: dl l2io0c14 » 6o5nbtrach15 Lom mie 
theses ibe ul 2 itty ee aee 


7° Subtract) os 2 125 Vl0 oS C8 hia) eens 
6 


8. Subtract : Lom LO eed 
2 6 


iOS sIOO 
(Se) 
ear 
= 


i 7 
2 Lc eae 
9, Pind 18 211 2. 8 See 2.) 2a eee 
these odd or even numbers ? : 
10. Willie always had as a present from his father one 
penny for each year he was old on his birthdays, and one 
more penny to help him grow. One year his father gave 
him fourteen pennies. How old was he that birthday ? 
11. Mary found ten eggs when she went to the barn. 
She broke one, bringing them to the house. But her 
mother gave her as many more as she needed to make 
thirteen in all. How many did her mother give her ? 
12. Write the Multiplication Table of Twos on the 
blackboard without any copy. 
13. Divide each even number from 2 to 24 by 2. Make 
a division table, beginning it lke this: 


45 ORAL TEACHING 
STUDY 


FORMS AND FRACTIONS 


1 x 1 inch. 1 x 14 inch. 


1 inch. 


1 inch. 


Rectangle. Rectangle. Right 
Square. Oblong. Angle. 


A rectangle is a form in which each angle is a right 
angle. A rectangle always has four sides. 

A square is a rectangle all of whose sides are equal. 

An oblong is any rectangle that is not a square. ‘The 
opposite sides of oblongs are always equal. 


A B C 


What is the name of the form A? B? (C? 
What is the name of the form 1? a? I? 
Point out 4 of A. 4o0f B. of C. 


Point out right angles in A, B, and @ 


splat Bat ad eas 


5. Make an oblong with sides one and two inches long. 
Divide it into two squares. 


6. Make another, and divide it into two triangles. 
Each square in 5 and each triangle in 6 is 4 of the 
oblong. 


STUDY AG 
ANSWER 

THREES 

3) 6) 9712) lOWIS Al eas Aiea SoO Soe 
0+3= 3 3+3= 6 
9+3=12 12+38=15 
18+3=21 21+ 38= 24 
27 +3= 380 30. + 3 = 33 


6+3= 9 
15+3=18 
24+ 3=27 
33 + 3 = 36 


Show by splints that each of these facts is true. 


a Quiles St eae EL 
8x2= 6 | 3x 8=24 
ae taicet) ol Sie ee aa et 
tle ues nnd By BX LOieaga0) 
sae ype ol bs) Dax eee 
SEO Selo Bx 12 36 


MULTIPLICATION TABLE OF THREES 


We read this, 3 1’s are 3, or three times one are three. 

444-412 “Three 4’s =Tfours 6) o-oo oo =i 

Are three 10’s 80? 10+10+10=30 Three 10’s=ten 3’s 
§84+84+3543438438434343+43=30 

1. Copy the Table of Threes on paper. 


2. Count by 3’s to 36. Write this counting in words, 
beginning, three, six, nine, and so on. 


3. Write the Table on the blackboard without any copy. 
4. Make a division table of threes, beginning it like this: 


3+38=1 


9+3=3 
oe 


6+38=2 


AT STUDY 
ANSWER 


THIRDS 


When anything is divided into three parts, each part 
is called a third. ‘Three thirds equal one whole. 


© LL Su 


Circle Rectangle Square Square 


Into how many parts is the circle divided? the rec- 
tangle ? each square ? 

Draw a line three inches long. Divide it into thirds. 

One third is written in figures 4. 

Two thirds are written in figures %. 

%4=|. Why is this true? Look and see. 

1. Eddie bought a cake and ate 4 of it. How much 
of the cake was left ? 

2. How many thirds are there in an orange ? 

3. How many thirds in two oranges? In one orange 
are three thirds. 2 times 3 are six thirds, §. 

4. 1 of 6 figs = how many figs? There are six times 
as many thirds in the 6 figs as there are in the one fig. 
6xi=§. §= 2. 

5. Whatis$of 6? tof 9? of 12? 

6. Which piece is the larger, 4 of a pie or $ of a pie? 

7. How much more does the whole of a cake cost than 
+ of it? | 

8. I started to walk to the depot. After I had walked 
} of the distance, what part of it had I still to walk ? 

9. If your mother gave you some money and you spent 
2 of it, what part of the money would you have left ? 


STUDY 48 
ANSWER 


TELLING QUANTITIES 


We buy and sell butter and cheese by pounds, but we 
measure potatoes and vinegar by quarts. Do you know 
how much a quart of anything is? A quart measure for 
dry things like flour is larger than that for liquids like 
milk. Six quarts of flour would take just a little more 
space than seven quarts of milk. A pint of flour, too, 
takes a little more space than a pint of milk. 


2 pints make 1 quart. 2 pts. = 1 qt. 
1 pint makes } quart. 1 pt. =4 qt. 
1. Mrs. Brown had three quarts of milk, and six hungry 


children. She gave each 3 pt. in a glass. How many 
quarts were left ? 


2. Willie bought a quart of peanuts, and gave one pint 
to his little brothers. What fraction of the quart did he 
keep himself ? 


4 quarts make 1 gallon. 4 gts. =1 gal. 
3. How many quarts are there in three gallons of oil? 


4. Susie’s mother had one gallon of maple syrup. One 
morning the family had three pints of maple syrup on the 
table for buckwheat cakes. How many pints were left in 
the gallon jug ? 


8 quarts make 1 peck. 

4 pecks make 1 bushel. 
8qts.=1pk. 4pks.=1bu. 32qts.=1bu. 64pts.=1 bu. 
4qts.=ipk. 2pks.=ibu. 16qts.=fbu. 16 pts.=1pk. 


49 STUDY 
ORAL 


QUANTITIES 


1. Willie bought 2 bushels of corn for his chickens, 
and fed them for 30 days 2 quarts each day. How many 
quarts were then left ? 

2. George bought 8 pecks of oats for his pony, and the 
grain dealer sent them in a 2-bushel bag, full. Was this 
correct ? 7 

3. A grocer had a barrel of apples. He sold 2 of them. 
What part of the barrel of apples did he have left ? 

4. One boy had two thirds of an apple, another boy 
had one third, and still another had one half of an apple. 
Tell how many parts of apples they had altogether. 

5. Two quarts of walnuts will fill how many cups, if 
each cup holds half a pint ? 

6. Filla gallon measure with water, using a pint meas- 
ure. How many times do you empty the pint measure ? 

7. How many quarts are there in 2 pecks? Which 
has more quarts, a peck or a gallon? Are the quarts the 
same in size ? 

8. A peck measure is one half full of oats. How many 
more quarts will it hold ? 

9. Henry filled a peck measure one quarter full of sand. 
How many quarts did he put into the measure? How many 
more quarts would it have held ? 

10. How many times must you empty a quart measure 
full of strawberries in order to fill a peck measure ? 

11. What part of a bushel of wheat is a peck of wheat ? 

12. What is the ratio of 1 to 4? If a bushel of oats 


—_—— 


costs a dollar, what will a peck of oats cost ? 
13. How many pints are there in 2 quarts? How many 
. pecks are there in 16 quarts? 


ORAL 50 


QUESTIONS 


How many gallons are there in 8 quarts ? 
How many pints are there in 3 quarts? 5 quarts ? 


How many pints are there in a gallon and a quart ? 


ed fot da 


How many quarts are there in a gallon and a quart? 
in a gallon and a pint ? 

5. If a pint of milk costs 4 cents, what will a quart 
cost? Ifa pint costs 3 cents, what will a gallon cost ? 

6. If milk is 3 cents a pint, what will a quart and a 
pint cost? At 3 cents a pint, what will two quarts cost? 

7. At 2 cents a pint, how many cents will half a gallon 
of skimmed milk cost ? 

8. Fred drinks a pint of milk every day. In how 
many days does he drink a gallon? At 3 cents a pint, how 
much will his milk cost for one week ? 

9. If vinegar is 8 ¢ a quart, how much will 4 pt. cost? 

10. My lamp burns a pint of kerosene every night. 
How many nights will a gallon last me ? 

11. A milkman has a gallon of cream. How many pint 
bottles can he fill from it ? 

12. Should 7 quarts of milk cost more than 2 gallons, 
or less? Why? 

13. A gallon jar is half full of water. I am going to 
fill it from a pint measure. How many times must I 
empty the measure ? 

14. A grocer had 10 quarts of syrup. He sold a gallon. 
How much syrup had he left ? 

15. Two gallons of oil will fill how many quart measures ? 

16. If you were paid 2 cents a pint for picking berries, 
how much money would you get for picking 5 quarts ? 


5] STUDY 


ANSWER 
SIXTEEN, 16 


We name ten and six things by the number sixteen. 


15+1=16 12+4=16 10+6=16 8+8=16 


We write sixteen with the figures 1 and 6, 16. 
We put the 1 in tens’ place by setting the 6 in 
units’ place. 

Show by splints that each of these number- 
facts is true: 10+6=16, 8+8=16, 44+12= 16, 
94+7=16, 11+5=16. 


~ 


44+4+4+4+4=16. How many 4’s are there in 16° 


24+242424+242+42+42. How many 2’s are there 
in 16? 8+8=16. How many 8’s do we find in 16? 


#x4—16 8x2=16 2x8=16 16+4=4. 16+2=8 


Count these dots: 


ele 
e@,\|¢e a 

“$F eens ers rere © e@eeoeoee 
re ejeleleleleieje @eeeee 
ele | | 

ele eecoeeeee 

ele cose eee 

ele | 


1. If eight girls in your school were sent this afternoon 
to the grocery by their mothers, each with two pennies to 
buy a yeast cake, how many pennies would all have to- 
gether ? 

2. Four boys spent sixteen cents for fishhooks: each 
spent _as much as the others. How many cents did each 


ee 


spend aD 


3. Mary had a nickel, Kate a dime, and Annie a penny. 
How many cents did they have altogether ? 


J 


STUDY 52 


SEVENTEEN, 17 


We name ten and seven things by the number seventeen. 


Seven and ten make seventeen. 104+7=17 
164-1=17) 15+2=1%) 9+ 3— 11 Sloot ii 
Show each of these facts by splints and counters. 


1. We cannot divide 17 by any smaller num- 
ber exactly, without remainder. 
We can divide 16 by 2, by 4, and by 8. 
We can divide 15 by 3 and by 5. 
We can divide 14 by 7 and by 2. 
We cannot divide 15 without remainder. 
We can divide 12 by 6, by 2, by 3, and by 4. 
We cannot divide 11 without remainder. 
We can divide 10 by 5 and by 2. 
We can divide 9 by 3. 
We can divide 8 by 4 and by 2. 
. We cannot divide 7 without remainder. 
We can divide 6 by 2 and by 3. 
We cannot divide 5 without remainder. 
14. We can divide 4 by 2. 


© HIN AAL YD 
@eeee ed 8 


Hee be 
Oo ye ng 


There are no multiplication or division facts to learn about 
Or c2 Oreo) OT O700 i sO eli One loa Ote seo tmUe 


About these numbers we learn only addition and sub- 
traction facts. 


15. ‘Tell number-stories about 17, using pennies, mar- 
bles, eggs, fish, dolls, apples, or whatever interests you, to 
show these facts: 10+7=17 154+2=17 ~ 17—11=6 
17-—-8=9 17-—8=14 17-—5=12 

16:2A dairy 6 4 T ah Ye 2 Hi 

D2 LD tS i Oe eo ee 


—_——- 


53 STUDY 
ANSWER 


EIGHTEEN, 18 


We name ten and eight things by the number eighteen. 


Eight and ten make eighteen. 10+8=18 . 

15+3=18 164+2=18 94+9=18 124+6=18 $, 

M2= 9 18+9= 2 9x2=18 2x9=18 § S 

1S3+6= 38 18+38= 6 6x3=18 38x6=18 § § 

Show each of these facts by splints and counters. $ § 

15 are three 5’s. 15 are ten and five. epr 

18 are three 6's. 18 are twelve and six. 

There are two 6’s in 12. fies aad 12+6=2. 
eee 

This group of dots ¢ : F is 2 times this group = - : 
Siete A HALF 
A DOZEN DOE 


18 are a dozen and a half dozen more. 
12 inches make one foot. 
18 inches are 12 inches and 6 inches more. 
18 inches are a foot and a half foot. 
Show these facts on the yardstick or by blackboard 
picture. 
NUMBER-STORIES 


1. John’s father asked him to get at the store a dozen 
and a half pens. ‘These cost one cent each. How many 
cents did John pay ? 


2. When John came home he found a yardstick and 
measured the kitten, which was 18 inches long from her 
nose to the end of her tail. How much was that-in feet ? 

3. Then his mother sent him on an errand to sell a 
dozen and a half of eggs. ‘The grocer gave him a dime 
a dozen. How many cents did he bring home ? 


ORAL 5A 
WRITTEN 


REVIEWS OF NUMBERS AND FORMS 


1. Tell number-stories about these facts: 


16+2=8 16 —6 =10 16+4= 4 
91+7=16 12+4=16 18 +3=16 
pele We te ac At See ye a 3. Subtract: 16 16 16 16 
14 11S F15 G7 OS LIers 


4. Subtract: 17 Lie até ibys Ah 17 bf 


rs 
ae 
ie 
= 
ro 
= 
| 4 


5. Dowhatthesigntells: 17 14 16 12 17 17 
—7T +3 +1 45 —2 —9 


GePAdd 2 1p wLOT as 7. Subtract: 18 18 18 18 
her trewlatle he 2 eae eet 


8. Divide 13 by 2, by 3, by 6, and by 9. 

9. Make stories about: 
16—3 18—9 At eee tea Lee 18— 10 
15+2 18—15 17—14. "10+7 15—5 1543 
18—6 17 —2 15=4 17—4 16—14 " “15— 


10. Draw an oblong 2 x 3 inches. | Divide it into halves. 
in several different ways. 

11. Draw another oblong of the same size. Divide it 
into thirds. 

12. Draw a triangle with one side of the right angle 
2 inches long and the other side 1 inch long. 

13. Draw a circle 1 inch in diameter and divide it into 
halves. A diameter is any straight lne through the 
center of a. circle: 


55 STUDY 
ANSWER 


NINETEEN, 19 


We name ten and nine things by the number nineteen. 
Nine and ten make nineteen. 10+9=19 
15+4=19 164+3=19 124+7=19 14+5=19 
18+1=19 54+54+544=19 4444444+43=19 
Show each of these facts by splints and counters. 


NUMBER-STORIES 


1. There were 19 boys in the school yard. 6 of them 
went home. How many were left ? 

2. 19 boys came to school early in the morning to play 
marbles. When they reached the school yard 2 of them 
found that they had lost their marbles on the way to 
school. How many had their marbles with them ? 

3. Nineteen girls were trying to cut paper dolls out 
of white paper. Fourteen of them made very nice dolls. 
How many of them were not able to make the dolls? 


4. Three times six boys went swimming. One more 
boy asked his mother if he could go, but she said, * No!” 
How many boys wanted to go? 

5. Eight times two girls walked home from school 
together in pairs. Three girls walked side by side. 
How many girls were there in all? 

6. Add: 12 11 14 7. 34+54+6+5= 8s. 104643= 


7 oO 


i o 9 9g. 84+443+44= Io 12+4+59+4+2= 


11. Subtract: 19 19 19 19 19 19 19 19 19 


| lo 

|e 
wt 
hosel 
bo 
wo 
= 
fend 
=P) 
0) 

| 


12. Tell number-stories about the facts in 7. 8, 9, 10, 
and 11. 


Van 


ORAL TEACHING 56 


ANSWER 
PARTITIONS 

3 8=2+1 

5 5=34+2 §5=24241 5=4+4+1 

4. (=d4+2 1=6+4+1 7=4+4+3 7=3+38+41 

11 11=74+4 11=8+3 1i=942 11=6+45 


11=5+4+5+41 11=3+3+4+341+41 11=44448 
13. 13=114+2 8=84+5 18=944 13=7+6 
13=54+5654+3 13={4+444+1 138=3+4+38+3+341 
18=2424242424241 13=10+4+3 
V7 17=138+4 17=54+54542 17=10+7 17=154+2 @ 
17=84+8+41 17=44+44444+41 17=12+5 
17=84+84+3434+842 17=164+1 17=74+7483 
19 19=174+2 19=54+54+54+4 19=164+3 19=14+5 
19=444444-44.3 19=34+34+34+343+43+41 
19=9+94+1 19=134+6 19=114+8 19=1049 


EEE 


1. Divide 3, 5, 7, 11, 18, 17, and 19 by 2, and show how 
many ones are left over. 

2)3 

dl 

2)17 

8 


+1, because 2x1=2 and 24+1=83 


+1, because 2 x 8=16 and 16+1=17 


2 JIVi lero aU lose emai ecb ane: 
oT + lun becaisees <4 1 oeandul eee 
3, Divide (ell 13 lie and 19 ae 
oe 


4. Divide 13, 17, and 19 by 7. 


sa hecalise wile a7 tate eee 


57 STUDY 


TWENTY, 20 


10+10=20 154+5=20 124+6+4+2= 20 
5+5+5+90= 20 6+6+6+4+2= 20 
Show each of these facts by splints and counters. 


We call two tens twenty. 


We write twenty in figures by putting 2 in tens’ 
J g yp 4 
place, and to show that 2 is in tens’ place, we set the zero, 
0, in units’ place. Write 20. 
Pp 


2x 10= 20 4xd5=20 3)20 + 2 


6 
There are six 3’s or three 6’s in 20 and 2 units over. 
We write this: (38 x 6)+ 2= 20 or (6 x 3)+2= 20. 
We place the marks of parenthesis ( ) around the 6 


and 3 to show that 3 multiples 6, not 6+ 2. If we wrote 
3 x 6+ 2, this would mean 3 times 8, for 6 + 2= 8. 


1. Find how many times 20 contains 3, 7, 9, with how 
many units over. 


2. Draw on the blackboard a square containing 20 
square inches. 


3. Add: perils toeeioeG. -4" 120 eieia 
T 8 


1 
Pogebt 2? 5) ee 16 


| eo 
sali 
om) 


4. Subtract: 20 20 20 20 20 20 20 20-20 20 
Ue LOS 12s Shee ar Ty Ag 


5. How would you divide twenty apples among five 
boys? among six boys? 

6. Can we divide twenty oranges among seven girls so 
that each may have as many as any other? How many 
would have only two? 


STUDY 
ANSWER 


FACTS 


OF 


All Additions : 


104+ 1=11 
104+ 2=12 
10+ 3=138 
104+ 4=14 
10+ 5=15 
10+ 6=16 
10+ T=17 
10+ 8=18 
10+ 9=19 
10+10=20 
11+ 1=12 


11+2=13 
11+38=14 
1S =16 
114+6=17 
11+7=18 
114+8=19 
114+ 9=20 
124+1=138 
12214 
12+38=15 


All Multiplications : 


2x6=12 
2xT=14 


2x8=16 
2x9=18 


Copy and answer : 


rhe hte 


OM 29 oP wN 
—ae 


25. 


20 20 


10. 
11. 
12. 
13. 


- § = 14. 


tis. 
16. 


ieee teen so-Ol. 


26. 4)16 


4)20 


58 


NUMBER, 11 TO 20 


124+4=16 
I2+5=17 
12+6=18 
iy eal 
12+8=20 
13--l=14 
Loo ip 
138+3=16 
18+4=17 
13+5=18 
13-+-6=19 


3x 4=12 


13+7=20 
144+1=15 
144+2=16 
14+-3=17T 
14-418 
14+5=19 
15+1=16 
15+2=17 
15+ 38=18 
154+4=19 


38x5=15 
3x6=18 


loo HRIoOo obo colbo AIR Ole 


15+5=20 
164+1=17 
16+2=18 
16+3=19 
16+4= 20 
17+1=18 
17+2=19 
17+3=20 
18+1=19 
18+2=20 
19-+1=20 


4x4=16 
4x5=20 


of 12= 
OD 14 
O bec 
Ole L Uj 
of sz 
oft y= 
. 18-54 6= 
. 1444+58-10= 
Subtract from 20 every number from 10 to 19. 


ANSWER 


= 


i ass 


SIGHT 60 
COUNTING 


1-20 


The teacher may make sight number cards, using ordi- 
nary paper or, better, drawing paper, 4 x 5 in. or 4 x 6 in 
size. The figures should be as large as those on page 4 for 
blackboard writing. They may be drawn with brush and 
diluted ink or with blue pencil. The children may make 
sets for themselves, either as large as the teacher’s set, or 
much smaller, 2 x 3 in., with figures as large as those on 
page 5. These sets of sight cards should review all the 
number facts as high as 20, and drill the pupil in quick 
recognition of number groups as high as 7 or even 10. 
The teacher with a set of cards in her hand may call for 
answers in various ways. The answers are to be remem- 
bered instantly and with certainty. 


For a set of sight-counting cards : 


10+1==|10+2=|10+3=|10+4=)10+5=|10+6=/10-+-7=|104 8=|10-+-9=/10+-10= 


10x2=| 42= | 2)10 | 5)10 |10+2=]10—1=]10—2=|10—3=|10—4=|10— 5= 


10—6=|10—7=|10—8=|10—9=/10)10 | 54+5=| 5X2=| 2x5=| 9+1=) 84+ 2= 


t+5=!| 6+4=—|18—8= 19—9=)1i is 16—6=|15—5= |14—4=|13—3=|12— 2= 


The variety of possible ways to use the numbers to 20 in combina- 
tions producing not more than 20 and using no partition facts or 
fractions over 4 is too great to permit of complete illustration. Not 
all the combinations or forms of signs to indicate operations involving 
10 are indicated even in these twenty spaces. 


61 ORAL TEACHING 
STUDY 


DAYS OF THE WEEK 


There are seven days in one week. After seven days 
we begin the names of the days over again. The names 
of the days are: Sunday, Monday, Tuesday, Wednesday, 
Thursday, Friday, Saturday. 

Each day is one seventh of a week. T days = 1 week. 

At midnight we change the name of the day. 


Many, many years ago, when our forefathers lived on the other side 
of the great Atlantic Ocean, most of them thought that the earth was 
ruled by beings who live in the sky. So they named each day for 
some one of these beings. We use their names for the days. 

Sunday is named for the Sun in the sky. 

Monday is named for the Moon in the sky. 

Tuesday is named for Tyr, who leads in battle. 

Wednesday is named for Woden, the wise father of all. 

Thursday is named for Thor, the thunder. 

Friday is named for Freya, the loving wife and mother. 

Saturday is named for Saturn, who began the world with time. 


ABBREVIATIONS 


Sunday Monday Tuesday Wednesday Thursday Friday Saturday 
Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 


Yesterday was the day before this day. 

To-day is this day we are now living in. 

To-morrow will be the day after this day. 

Day before yesterday was two days ago. 

Day after to-morrow will be two days after this. 

A fortnight is two weeks, or fourteen nights or days. 


1. What day will be ten days from to-day? What day 
was ten days ago ? ; 


2. Name the days when we go to school. 


ORAL 62 


QUESTIONS 


1. A man has a dozen letters to be mailed and only four 
stamps. How many stamps must he buy ? 

2. How many cents are 10¢ and 2¢? 10¢ and 4¢? 
16% and 1¢? 3% and 10¢? 14¢ and 5¢? 18¢ and 3¢? 
12¢ and 8? 13¢less5¢? 19% less 7? 

3. Make 12 dots ina row. Make 2 more dots under 
them. How many dots in all have you made? Add 5 
more. How many have you made now? 

4. Nine boys have twenty marbles. Four of them 
have ten marbles altogether. Each of the rest has as 
many as any of the others. How many marbles has each 
of these ? 

5. Count by 2’s from 1 to 19 and from 19 back to 1. 
Count by 3’s from 19 backwards to 1. 

Count by 3’s from 1 to 19. 
Count by 4’s from 0 to 20 and from 20 back to 0. 
Count by 4’s from 17 back to 1. 

10. Count by 2’s from 3 to 19 and from 19 back to 38. 

11. Count by 3’s from 2 to 20 and from 20 back to 2. 

12. Count by 4’s from 5 to 17. 

13. Count backwards by 5’s from 20 to 0. 

14. Count backwards by 5’s from 19 to 4. 

15. Count by 6’s from 0 to 18 and back from 18 to 0. 

16. Count by 7’s to 20, beginning at 38. What is the 
highest number we reach ? 

17. Count by 5’s to 20, beginning at 4. What is the 
highest number we reach ? 

1s. Count by 4’s to 20, beginning at 2. What is the 
highest number we reach ? 


om ao 


63 ORAL 


REVIEW 


1. Lay 1 bundle of 10 splints. Count out ten loose 
ones and tie them into a bundle. How many splints are 
there in the two bundles? Write the number 20. What 
does the zero mean? Have you any loose splints when 
you show 20 in bundles of ten splints ? 

2. How many figures do you write for eleven? for 
twelve? for thirteen? for twenty ? 

3. In all these numbers, what does the figure on the 
left show? What does the figure on the right show ? 

4. While Mary was feeding 7 birds 4 more birds came. 
Then how many birds were there ? 

5. There are 9 cups in 1 row, and 4 cups in another 
row. How many cups are there in both rows ? 

6. 10 pencils and 2 pencils are how many pencils ? 

7. Jennie had a dime and 2%. She spent 4 of her 
money. How many cents did she have left ? 

8. How many marbles must you put with 9 marbles in 
order to have 14 marbles ? 

9. I have four dollars. How many more dollars must I 
get in order to have fifteen dollars ? 

10. Edwin had 13 marbles. He lost 5. How many 
had he left ? 

11. Make 2 triangles. Under them make 2 squares. 
How many sides are there in the triangles? How many 
sides in the square? How many sides altogether in all 
the squares and triangles ? 

12. An orchard has 10 apple trees and 4 pear trees. 
How many trees are there in the orchard ? 

13. Henry has ten cents. How many more cents must 
he get in order to have 14¢? 


ORAL 64 
WRITTEN 


QUESTIONS 


1. Write the numbers made up of : 

One 10 and 7 units. One 10 and 3 units. One 10 and 
6 units. One 10 and d5units. One 10 and 8 units. One 
10 and 2 units. One 10 and 1 unit. One 10 and 4 units. 
One 10 and 9 units. One10. Two 10’s. 

Seven units. Three units. Eight units. Six units. 
Five units. Nine units. 

2. A farmer had 19 animals in a field. 8 of them 
were sheep and the rest were cows. How many cows 
were there in the field? 

3. Ella has 11¢ and Maud has 17%. How many more 
cents has Maud than Ella? 

4. Alice had 19 splints in her hand. She put 7 of 
them on her desk. How many splints did she keep in 
her hand? } 

5. I had 20 and lost 6. How many cents had I left ? 

6. Mrs. Smith paid $16 for a jacket and $4 for a hat. 
How many dollars did she spend ? 

7. A farmer had 19 chickens. He sold 5 of them. 
How many were left ? 

8. There were 20 barrels of flour in astore. 6 of them 
were sold. How many were left ? 

9. One ladder has 19 rungs. Another ladder has 14 
rungs. What number tells the difference in rungs be- 
tween the ladders ? 

10. I paid 3¢ for a pencil and 16¢ for paper. How 
many cents did I spend ? 

11. Emma had 20¢. She paid 2 nickels in car fares. 
How much money had she left ? 


12. 12 lemon pies and 7 peach pies are how many pies ? 


65 DRILL 
BUSY WORK 


SUBTRACTING 


1. John had 10 cents, and spent 7 cents for a whistle. 
He had three cents left. 

2. Mary had 16 paper dolls, and gave away 11. She 
kept 5 for herself. 

Give each boy and girl one combination to tell or write 
a story about. 


3—2 — 


o— 3 5—1 3—1 12—6 
4 — 3 9 — 4 6— 2 9— 6 7—6 
3—1 2—2 9—5 12—8 13 — 9 
8— 5 7—4 6 — 6 9—8 o— 5 
8 — 4 15 —9 16—7 11—5 4—2 
12-9 11—8 1-7 4—1] 6—3 
10—3 3-3 1-1 8 — 7 9 — 4 
9—8 13 —8 17 —9 9-9 20 — 6 
11 — 4 8 — 38 10 —1 20 — 1 14—5 
4—4 15 — 6 9—3 13 —7 20 —8 
6 — 1 12—5 13 — 5 14-8 16 —9 
6—9d 13 — 6 10— 8 11 — 38 13 — 4 
10 —9 7—1 8—8 18 — 9 10 —3 
T— 3 o—2 20 — 2 11-9 14—6 
7T—5 8 — 1 10 —4 10 —7 10 —5 
5—4 2—1 |. 12-4 20 — 3 15—8 
9—1 11—2 14—T7 17 —8 12-7 
7T—2 18 — 8 20 — 7 20 — 9 20 — 5 
9—2 14-9 20 — 4 11 —7 16—8 
10 — 6 12-3 11 —6 10—10| 15—7 


3. Write out the answers to the questions in each col- 
umn: 3—2=1,5-—38=2. 


4. Tell the answers, taking turns around the class. 


ORAL TEACHING 66 
STUDY 


RATIOS 


Alisiorx CPEs pe GC. 

CistofA. Cis of B. 

We say that 5 is the ratzo of A to C; 
and that 3 is the ratio of B to C. Ratio 
C_ means how large anything is compared 
LJ with anything else. We say that 4 1s 
5 3 1 the ratio of C to A; and that 4 is the 
ratio of (to B. This means that Cis 4 of A and 4 of B. 

D K FR 
GEEBEHE 
ee 1 


What is the ratio of F to D? of Eto D? of Dto H? of 
DOr ol LD to keh 


@ 

e The ratio of 6 to 1 is 6. 
aie The ratio of 4 to 1 is 4. 
od The ratio of 2 to 1 is 2. 
e@ee2e @ 


The ratio of 1 to 2is 4. Why? 

The ratio of lto4is+. Why? 

The ratio of 1 to 6 is}. Why? 

In the forms A, 6, and C the ratio of B to A is 3, 
because B is 3 of A. The ratio of A to B is 3, because A 
is (8 + 2) of B. 

The ratio of 4 to 6 things is 4, because 1 is 3 of 6 and 
there are 4 x 1 thing in 4 things. The ratio of 6 to 4 is §, 
because | is + of 4 and there are 6 x 1 thing in 6 things. 


2. oWehat 18 ‘the ratioVotalston(sctohels ton wrote Losec 
OF [to 2% “Of 3 to 12 Ole (et08e PeOln onto al Ure O tal ate ee 
2. Find the ratio of 4 to 8, 16, 12, 2, 20. 


67 ORAL 


QUESTIONS 


1. I have 8 black chicks and 5 times as many white 
ones. How many white chicks have I? 

2. How many figs are 3 times 4 figs? 5 times 3 figs ? 

3. 4 pictures cost $5 apiece. How many dollars did 
they all cost ? 

4. A roll of braid costs 16¢. What will be the price 
of one quarter of the roll ? 

5. Helen had 12%. She gave } of her money to her 
sister Alice. How many cents did she give to Alice ? 

6. If Charles can ride 20 miles in 1 hour on his wheel, 
how far can he ride in a quarter of an hour ? 

7. If you bought } of a dozen of bananas, how many 
bananas would you have? how many if you bought ? of 
a dozen? how many if you bought 3 of a dozen? 


s. A man walks 4 miles an hour. How far does he 
walk in 4 hours? in 5 hours? in 42 hours ? 


9. Edgar had 6%. Arthur has 3 times as much money 
as Edgar. How many cents has Arthur ? 


10. If we use 5 crayons a day in this room, how long 
will 18 crayons last us ? 

11. If a man worked only half the working days in a 
week, how many days would he be idle? How many days 
would he be at work ? 

12. If you walk 1 mile every school day, how many 
miles do you walk in a week? If the walk is 1 mile each 
way, how many miles do you walk in a week, when you 
stay at school for noon-recess ? 

13. During Christmas week I was at home only 2 days. 
How many days was I away from home ? 


69 STUDY THE 
PICTURE 


RATIOS 


1. Do you see 4 balls or spheres together? Is there 1 
ball near them? Do yousee the 3 balls hanging from the 
door? How many balls do you see in all ? 

2. Do you see five piles of cylinders and one single 
cylinder? Count the number of cylinders in each pile. 

3. Do you see six piles of cubes? Count the number 
of cubes in each pile. Do you see one cube separate from 
the rest ? 

4. Point to 1 cube and 7 cubes. 1 cube x 7 = 7 cubes. 
T cubes + 1=7. ‘The ratio or number relation of T cubes 
to 1 cube is 7. The ratio or number relation of 1 cube to 
7 cubes is 4, one seventh. 

5. Point to 2 cubes and 6 cubes. 2 cubes x 5=6 cubes, 
6 cubes +2=3. The ratio of 6 cubes to 2 cubes is 3. 
The ratio of 2 cubes to 6 cubes is 4, one third. 

6. Point to 1 sphere and to 8 spheres. 1 sphere x 8=8 
spheres. 8 spheres+1=8. ‘The ratio of 8 spheres to 1 
sphere is 8. The ratio of 1 sphere to 8 spheres is }, one 
eighth. 

7. Point to 4 cubes and 6 cubes. ‘The ratio of 4 cubes 
to 6 cubes is 4, four sixths. The ratio of 6 cubes to 4 
cubes is §, six fourths. | 

8. Point to 2 cubes, to 4 cubes, to 3 cubes, and to 6 cubes. 

9. How much higher is the pile of 4 cubes than the 
pile of 2 cubes ? 

10. How much higher is the pile of 6 cubes than the 
pile of 53 cubes ? 

11. How high is the pile of 2 cubes compared with 
the pile of 4 cubes ? 

12. How high is the pile of 5 cubes compared with the 


pile of 6 cubes ? 


STUDY 70 


ANSWER 
FOURS 
4 8 12 16 20 24 28 32 36 40 44 48 
0O+4= 4 4+4= 8 8+4=12 
24+4+4= 28 284+4= 32 32+4+4= 36 
12+4=16 16+4 = 20 20 +4 = 24 
36 +4= 40 40+4= 44 444+4=48 
Show by splints that each of these facts is true. 
Lc Leet Ae tigen 
txt Zens AST 8 oe 
fx =a hee Mas ale 
4x4=16 4x 10=40 
4x5=20 4xlil=44 
rs 4x12=48 


MULTIPLICATION TABLE OF FouURS 


We read this, 4 1’s are 4, or four times one are four. 
§6+5+5+5=20 45’s=654s 444444444=20 
Are 4 8’s 32? 84+84+84+8=382 
4 8's=8 4’s 44+44+44444444444=32 
1. Copy the Table of Fours on paper. 2. Learn Fours. 
3. Show that 4 1’s=4, 4 4’s=16, 4 (s=23, 4 2is=8, 
4 6’s=24, 4 9’'s=386, 4 -3’s=12, 4 10’s=40, 4 1l’s=44. 
4. Write the Table on the blackboard without any copy. 
5. Make a division table of fours, beginning it like this: 


12+4=8 | 20+ 


16+4=4 


8+-4=—2 


71 STUDY 
ANSWER 


FOURTHS OR QUARTERS 


When anything is divided into four parts, each part is 
called a fourth ora aes en fourths or four quarters 
make one whole. 


SHIEK 


Circle Rectangle Rectangle Square 


Into how many parts is the circle divided? Each 
rectangle ? 

Into how many parts is the square divided ? 

How many fourths are there in each of these forms ? 

4=1. Four quarters are one. One half of four . 2. 


4+2=2. One half of four fourths is two fourths. 4 of 
4=—2; $=1; §=1; ¢=1; 4=2. Read each of ae | 


facts in words. 
1. Make three rec- 


tangles, each one inch 
high by two inches 
long. Cut one rec- 


tangle into halves. 
Cut the second rectangle into fourths. Place the halves 
upon the third rectangle, and the fourths upon the halves. 
Are the two halves equal to the four fourths? Are the two 
halves and the four fourths equal to the third rectangle ? 
2. Willie had a quarter of a dollar, his aunt gave him 
half a dollar. How many quarters of a dollar did he have 
then? How many fourths of a dollar ? 
3. A barrel of flour contains how many fourths of a 
barrel? If ? of the flour are taken out of the barrel, how 
much of the flour is left in the barrel ? 


ORAL TEACHING rey 
ANSWER 


TELLING WEIGHTS 


Did you ever buy anything at a store? Did you ever 
notice how much heavier 5 pounds of sugar are than 2 
pounds of coffee? Did you ever lift a piece of iron 
weighing just one pound ? 

We buy some things by their weight or heaviness. 

One pound is the standard measure of weight, just as 
a foot is for length, an hour for time, and a quart for 
quantity or amount. 


16 ounces (oz. ) make 1 pound (1b. ). 
1 oz. = 5); lb. 1otb e==sl'b.07. 4 lb. = 8 oz. 


1. Name five things sold by weight. 

2. If a pound of meat costs 20%, what will 1 of a 
pound cost ? 

3. A melon weighs 20 ounces. How many more ounces 
than 1 pound does it weigh ? 

4. What is the ratio of 4 ounces to 16 ounces ? 

5. If a pound of candy costs 20%, how much will a 
quarter of a pound cost? How much will 3 of a pound 
cost ? 

6. If Mr. Brown and his family use 3 pounds of sugar 
in 4 days, how many ounces do they use in 1 day? 

7. How many ounce weights are equal to a quarter of 
a pound weight ? 

8g. If a quarter of a pound of coffee costs 9¢, how many 
cents will a pound cost ? 

9. At 16¥¢ a pound, what will half a pound of crackers 
cost ? 

10. When pepper is 6 an ounce, can you buy half 
a pound of pepper for half a dollar? 


73 ORAL 
WRITTEN 


REVIEWS 


1. Can you see that the 2 cubes in the picture on 
page 68 are 2 of the 3 cubes, and that the 8 cubes are 3 
of the 2 cubes? 


2. Make all the comparisons you can of these cylin- 
ders, cubes, and spheres. You are finding ratios. 


3. Draw on paper forms, and write on paper dots, to 


show these ratios: 6, 3, 2, 4, 4, 4. 


4. Make forms on the blackboard to show these ratios : 
6, 4, 2 4, 3s 4. 

5. Which is the last day of the week? The first day ? 
The second day? The fourth day? The sixth day? 


The seventh day? The fifth day ? 


6. A man worked on Thursday, Friday, and Saturday. 
He was paid two dollars for every day he worked. How 
many dollars did he get ? 

7. Arthur and Fred ate 3 of a cake. They gave the 
rest away. What part of the cake did they give away ? 


8. Hattie had ? of a dollar. She spent 3 of a dollar 
for a doll. How much money had she left ? 


9. Fred gave } of his orange to Willie, and another } 
to Frank. He ate another +. How much of the orange 
did he have left ? 


10. John was sent to the grocery to buy 2 ounces of 
pepper, 1 pound of coffee, 4 pound of tea, $ pound of 
cinnamon, and 3 pounds of sugar. How many pounds 
did he carry home to his mother ? 

11. Mary had 25 cents with which to buy 4 lbs. of sugar 
at 5¢a pound, and } lb. of chocolate cream candy at 20 fa 
pound. Did she have enough money to buy these things ? 


STUDY 74 


NUMBERS TWENTY-ONE TO TWENTY-FIVE 
al 


Twenty things and one thing we call by the $ § 
number twenty-one. ore 
10+1041=21 20+1=21 164+5=21 pe 
15+6=21 10+11=21 12+9=21 18+38=21 ¢¢ 

We write the two in tens’ place and the 1 in oree, 
units’ place. 

ap 22 

ee Twenty and two we call twenty-two. 

se © 204-104 2 = 22 20+ 2= 22 164+6=22 
Sine 154+7=22 104+12=22 18+4=22 
ee 144+ 8=22 2x tlie 22 22+11=2 
@®ee 93 ° ° 

Twenty and three we call twenty-three. pate 
10+1043=238 20+3= 23 16+7=23 $8 
154+ 8= 238 104 13= 23 18+5=23 96 | 
1449=23 238=(4x5)+3 23=(6x3)+5 98 8 

ee 94 
® @ 
oe Twenty and four we call twenty-four. 
sis 104+104+4=24 20 +4 = 24 164+8=24 
Ereie 154 9= 24 104+14=24 18+6= 24 
ere’ 144+10=24 6x4=24 12x 2=24 
25 ee 
Twenty and five we call twenty-five. ate 
oo [Seo [feo [Sl [Sf 5 5's ore 25. 8 8 
10+104+5=25 5x5=25 25+5=5 2441=25 § § ¢ 
(6x4)4+1=25 (8x7)4+4=25 (8x3)4+1=25 $$ $ 


m5 STUDY 


NUMBERS TWENTY-SIX TO TWENTY-NINE 
26 


Twenty things and six things we call by the 
number twenty-six. 


© 10+10+6=26 204+6=26 16+10= 26 
© 154+11=26 124 14=26 18 +8=26 
§ 19+7=26 26=(5x5)+1 26=(8x8)+2 
27 of 
Twenty and seven we call twenty-seven. <5° 
‘i @es 
104+104+7=27 204+7=27 164 11=27 Acq S 
154+12=27 10417=27 184+9=27 ome 
14413= 27 Seat (6x4)+3=27 $88 
wg be 28 
e3°e 
5h aba Twenty and eight we call twenty-eight. 
eee 1041048528 20+4+8=28 164+12=28 
erste Lot) = 28 14+14=28 18410=28 
Pee Oe) 7x4=2 5x 5 sty 
eee 19+9=28 ae (5x 5)+38=28 
ra cee 
Twenty and nine we call twenty-nine. iB 
10+1049=29 204+9=29 16+13=29 pe 
15+14=29 18+11=29 19+10=29 pide 
(Tx4)+1=29 (2x10)+9=29 (8x3)+5=29 9 ee 


1. Tell number-stories about all the facts on pages 66 
and 67. 

2. Copy on the blackboard the facts on pages 66 and 67. 

3. Show all the facts on pages 66 and 67 with splints, 
pennies, and counters. 


STUDY | "6 
ANSWER 


Zee O} 29 


Twenty-one 21 ‘Twenty-two 22 Twenty-three 23 
Twenty-four 24 Twenty-five 25 Twenty-six 26 
Twenty-seven 27 Twenty-eight 28 Twenty-nine 29 
1. How many 10’s are there in 21? What is left over ? 
2. How many 10’sare there in 24? What are left over? 
3. How many 10’s and how many units, or ones, are 
there in 23? in 22? in 27? in 26? in 25? in 28? in 297? 
eee ee ee | HOW many rows) Ol ieedotcmare 
eeeeece there? of 3 dots? How many dots 
© Peet ets OS cares Noreen cle 
§&. 38xf=? T474T=? 38484384384843843=? 
How many 7’sin 21? Whatis+of 21? What is 4 of 21? 
How many 3’s in 21? (xds? 121 3)21 


$ is the sign for a dollar of money. 

6. A dealer sold 7 hats at $3 each? How many dollars 
did he get ? 

7. There were 21 apples in a barrel. I took out 4 of 
them. How many apples did I take out? 

8. Ethel gave 2 dimes and a cent for 3 yards of braid. 
What was the price of the braid a yard ? 

9. 17+7T=? If we wish to do so, we can find the 
answer by these steps: 

17 +3 = 20 7T—3=4 20 +4 = 24 


10. 18+6=? 1842=20 6-—-2=4 20+4=24 
JBL AN ORea es: 7 6 2 8 1 4) i) 4 
6 3 2 fi 3 2 2 5) 3 
4 5 2 14 5 2 Oi hla: 5 
2 d 11 1 5 1 5) Se Fs10 
pat 3 1 3 ie ae 1 3 


7 ORAL 
WRITTEN 


QUESTIONS 
One quarter of a dollar = 25¢ 


1. Etta bought 8 lead pencils at 3% apiece. She gave 
the clerk a quarter. What change should she get ? 

_2. Mrs. Brown bought 3 pounds of currants at 8% a 
pound. She gave the clerk 2 dimes and a-nickel. What 
change should she get ? 

3. At 3¢a yard, how much will 7 yards of braid cost ? 
at 4¢a yard? at 5¢? at 6¢? 

4. Mr. Jones divided 18 boxes of figs equally among 6 
children. How many boxes did each child get ? 

5. Irene had 9%. She spent } of her money, and gave 
another 4 to her brother. What part of her money had 
she left? How many cents had she left ? 

6. A farmer sold half a bushel of pears to one man and 
a fourth of a bushel to another man. How many fourths 
in all did he sell ? 

7. How many quarters of a dollar make a dollar? a 
dollar and a quarter? a dollar and a half? a dollar and 
three quarters ? two dollars ? 

8. Two halves of a pie were each cut into two equal 
parts. Henry ate one of those parts. What part of the 
whole pie was left ? 

9. Mary bought a yard of ribbon, and used 2 of it. 
What part of the yard of ribbon was left ? 

10. Willie is twice as old as Charles. Willie is 14 years 
old. How old is Charles ? 

11. In an orchard there are 15 peach trees and 12 pear 
trees. How many trees are there in the orchard ? 

12. In a can there are 2 gallons of milk. How many 
pints are there? 


STUDY 78 
ANSWER 


20 AND 25 


de 2x10=? « AObG2 =v. (20e 10 2) SNe, 
2. What is 4 of 20? +, of 20? 4 of 20? + of 20? 
of 20? 8, of 20? 8 of 20? 9% of 20? 

3. What is the ratio of 20 to 10? of 10 to 20? 

4. Edna bought a yard of lace for 18¢. She gave the 
clerk 2 dimes. What change should he give her ? 


io 0 


5. How many dots are there in each of 
these rows? .How many rows are there? 
How many dots are there in all? 


6. 5x5=? How many 5’s are there in 
25? How many o’s are there in 20? 

7. What is the ratio of 25 to 5? of 20 to 5? of 5 to 
20? of 5 to 25? 

25+5=? 20+5=? 10+5=? 
At 5% each, how many cents will 5 oranges cost ? 

10. How many nickels equal a quarter of a dollar ? 

Ww. 7+8410—5=? 25—5—5—5=? 

12. 14+17—-10—5+4+2=? 28-—38-—-544+41=? 

13. 16+4+5—6—4=? 24—3-2+46=? 

14. If one table costs $5, how many dollars will 2 tables 
cost? How many $5 in $10? 

15. What is the cost of 5 hats at $4 each ? 

16. Ella has 25%. How many paper dolls at 2¢ apiece 
can she buy ? 

17. How much money will she have left, after buying 
all the dolls she can at that ee ? 

1s, Multiply 1,°3,,.7502.00.58. 4.6) onnL0, 2 stays ce 

19. Multiply 1, 4, 7, 6 Bina : Panis way 

20. Multiply 5, 2, 1, 4, 3, by 5. 


79 


QUESTIONS 


1 84+44+44+3=? 
io aD oe? 
29-—8+1-—2-—10-—4-1=? 
28 —8+14+24+2-—4-1=? 
20 —10+2-—38+4-1+4+5-—3=? 
22 —20+4+4+10-—2—-— 


jody (SE) ee eS ee 


2. Add: 


Wea ee 


RH oO 


| bo 


3. Count from: 


0 by 8's to 
0 by 11's to 
1 by 3's to 
1 by 6's to 


24 
22 
26 
25 


4 by 3's to 25 
6 by 3's to 27 
5 by 2’s to 29 
4. How many: 
Zein soto LO 
Bsn cote 22 
4’sin 12? 24? 
Pe Mind 2 
(sin 21? 14? 
sin 27? 18? 
It’s in’ 22? 


} Or em dO SO bO 


0 by 
0 by 
0 by 
0 by 
2 by 
1 by 
) by 
2 by 


16? 
18?. 
16? 
15? 
28 ? 
9? 


DSi ee) a 


29-—1—7—-1=? 


ORAL 


1—5—4-—-3=? 
3 9 5 7 
7 1 4 2 
| + 3 3 
2 3 6 6 
1 6 D 1 
3's to 27 0 by 4’s to 
6’s to 24 0 by T’s to 
9’s to 27 0 by 10’s to 
12’s to 24 1 by 3's to 
4’s to 28 EL bye CO sn00 
Us to 29 38 by 2’s to 
6’s to 29 2-by 7s to 
o’s to 27 3 by 4’s to 
20? 14? 12? 24? 22? 
UA 2415 a? 
20? 28? 
20? 6’sin 18? 24? 
8’s in 24? 16? 
10’s in 20? 10? 


12’s in. 24? 


i) 

8 

6 

7 

3 
28 
28 
20 
23 
26 
29 
23 
27 

12? 

8? 


WRITTEN . 80 


LeTO}.29 

Copy and add by rows and columns: 

Ls 2. 
eer ae 2 Lo eo eee Snellen. 48155 
Gaesdie (9s 27g eee Zh Ose i tates 
Dee ile teres the Sal mal 
eee a ae ee yam grees el Be 27 
che Oy ey eae Raley’, ed | 1a died ber ihe to). 
PRG oe Ete vd oes! Sel al ): {0k mame. 
Al: ete cL ae 2 mere) aed 22 104 SOeselamno 
Copy and complete : 

3. 4. 5. 

ttc 6 ea eee 1S bas 22 = 
It Seay 25 =a ot LO xe: 25 = 
Ee a 1 Diestaxey. ae 1Gi 
PAVE USS eor4 Le a: pan 2K? Le 
LU exae Wea a flee ca Lia) 
BU nL Uaxe? ee Pa i Shs 24 = 

7, 9—-1+2—38-—4+64+8-10=—. 

27 -6—1—1042-—8+44-—2=—. 


LOSE 198 SB Se Reet oe ees 
Br 04 me) 2 Ge ae eee 
108 10 a eG eae 


Doth Uist Dire BLU cee 
9. 28—8-—4-—3-—3- 
26-—-6—5—4-—3— 


$29 Se 
Bas meen 
ee ee 


DOTS Ge Osler] Greer tensa] (ye [) eee 


10. Try these questions: 
(0x 2)+6=? 


(25+5)+3=? 
2+4+(3x6)=10 x? 


H bo 


H DO DO RR Or 


8] ORAL 


REVIEW 


We found that of the numbers below 20, these cannot 
be evenly divided by any other number,— 1, 2, 3, 5, 7, 11, 
138, 17, 19. Of the numbers 20 to 29, these cannot be 
divided by any other number, — 23, 29. By “evenly 
divided ” we mean that the number can be divided with 
no units left over. 


QUESTIONS 


1. A table is 4 feet in length. A bench is 4 times as 
long. How long is the bench ? 

2. George is 27 years old. James is 6 years younger. 
How old is James ? 

3. If a gallon of water weighs 10 pounds, how many 
pounds will ten gallons of water weigh? How many 
pounds will half a gallon weigh? How many pounds will 
1 quart weigh ? 

4. How many ounces are there in half a pound of meat? 

5. 6. if 8. “ j 
eu ee Leet te Koa OK Lt DX eat 
pee Kiet Ar Qat: (Ox 10 tO Xa 


B2xXx%=? 2x 56=? 2xlQ=—? Bx B=? 2Pxdb=? 
6x38=? 4x 5=? 8x 5=? 9x 2=? 2xT=? 
5x5=? 2x 8=? 5x 2=? 4x 4=? 2x2=? 


ate ee ee booed ce 7h 6K) i 8 KL? 
exis, Ox (iat “ox 2 2x Doh 4 x 6 =? 
Poesia ox 2, 2k f=? 6x Z=? 38x 3=—7? 
Seat eee kot! 2X b= OX Geet. 4 Dee 
iebenit wear Ce eee x 4m fea?) 4 ee? 
pee ee ee ie BK 9 = 7 S22? 8 x 3=? 


~ 


STUDY 89 
ANSWER 


THE NUMBERS THIRTY TO NINETY-NINE 


We call three tens thirty and four tens forty. 
10 L010 = BO eee LOM LU a ee 
20+10=30. es 2 x 20 = 40. °° 

We write thirty with § - Wewrite forty with sie 

3 in tens’ place and 0 in § § § ate 
units’ place. ece ee 
eee ee 


4 in tens’ place and 
0 in units’ place. 


TABLE OF TENS, ADDING UNITS 


eeeeoe0e ee 10 + e@ at 
e@eeeee @e 20 + ee 22 
eeeooce ee 30 + eee a OD: 
eoeeee ee 40 + eooee8e = 44 
eeee0e ee 50 + @eecoeec5ne iy = spe 
ecoceoeceoceee 6) + eo5veee ae 66 
eecoeoeee ee 70 + evoocececce = SY 
ecoecoe ec 80 + eov5uvcece =) SS 
eeoeeed ee 90 + eooeveveve2e0 = 99 
eeoeeece e 99 + e — KD 


We write nine, J; ten, |Q; nineteen, |G; twenty, 
2O; twenty-nine, 2; thirty, 30. Then we write 
forty,w Lt Os fifty, BoA) 5, esixty, bo: seventy, a] (Os 
eighty, &Q; ninety, q QO; but after ninety-nine, 99, we 
write one hundred, |OO. 

1 ten is written | QO; 2 tens are written 20; 8 tens, 


30; 4tens, 10; 5tens, 50; 6 tens, bQ; 7 tens, q Os: 
8 tens, §(); 9 tens, GO; but 10 tens are written (00: 


83 ORAL 


QUESTIONS 


1. If 20 barrels of apples cost $40, how much will 1 
barrel cost ? 

2. Charles had 47%. He paid 5¢ for car fare. How 
many cents had he left ? 

3. A grocer had 66 eggs. He sold half adozen. How 
many eggs did he have left ? 

4. At 50¢ a dozen, how many oranges can you buy for 
100, or $1? 

5. I bought 9 rocking-chairs at $10 each, and 1 table 
for $8. How much money did I spend ? 

6. Mrs. Smith bought 3 pounds of coffee for 30% a 
pound, and 1 cake of soap for 5%. She gave the clerk 
a dollar bill. What change should she get ? 

7. At 20¢ a dozen, what will be the cost of 4 dozens 
of eggs? 

8. Ella bought 2 pounds of meat at 20%a pound. What 
change should she get out of a fifty-cent piece which she 
gave in payment ? 

9. A rug cost thirty dollars and a bookcase forty dol- 
lars. What was the cost of both articles ? 

1o. If a train goes 30 miles in an hour, how many miles 
will it go in three hours ? 

11. I had 57¢ and spent 6%. What had I left? 

12. If a bushel of peas weighs 60 pounds, how many 
pounds does half a bushel weigh? How many pounds 
does a bushel and a half weigh ? 

13. A yard of silk cost $1. How many cents will half 
a yard cost ? 

14. George had 80%. He spent } of his money. How 
many cents did he spend ? 


ORAL SA 


REVIEW 


1. Count forwards to 100, beginning at 1. 
2. Count backwards to 1, beginning at 100. 


3. Make tables of tens, adding various numbers of 
units. 


4. Count to one hundred in writing, using words, not 
figures. 

How many times are 2 contained in 10, 12, 24, 20,16? 

6. How many times are 8 contained in Oe 21s Los 2 neha 

7. How many times are 4 contained in LG, 242055 noe 

8. How many times are 5 contained in 10220, loeeom 

9 


How many times are 6 contained in 24, 12, 18 ? 


10. 1 ily 12. 13. 14; 
12+2=? 6+8=? 2422=? 24+ 8=? 24+12=? 
24+4=? 15+5=? 18+38=? 12+ 4=? 18+ 2=? 
20+4=? 6+5=? 8+2=? 22+11=? 16+ 6=? 
24+-6=? 10+29=? 16+2=? 25+ 5=? 18+ 6=? - 
21-7T=? 12+38=? 28+7=? 27+ 9=? 20+10=? 
W2-l=? d0+5=? 2le38=2?7 22— 2=/ levee 
24+8=? 27+38=? 28+4=? 14+ T=? 20+ 2=? 


15. Mr. Brown is 87 years old, and his son Fred is 6 
years old. How many years older than Fred is his father? 

16. Charles wants to buy a ball that costs 15%. He has 
a dime. How many more cents does he need to buy the 
ball ? 

17. A teacher had 16 pens. She gave 10 of them to her 
pupils. How many pens did she keep ? 

1s. From a ribbon 17 inches in length 15 inches were 
cut off. How many inches were left ? 


85 ORAL TEACHING 
WRITTEN 


SUBTRACTING 


73 Lay out 73 splints, 7 bundles of ten, and 3 loose 
9 splints. Untie 1 bundle, leaving 6 bundles tied. 
— Add the untied 10 to the 3 loose splints, making 13 
splints. Take 8 away from 13, 5 are left. Take 
2 bundles away from the 6 bundles, 4 are left. 4 
bundles of 10 splints and 5 loose splints are 45 splints. 
(4 tens and 5 units are 45.) 
9 We cannot take 6 units from 5 units. We take 
3 1 ten from the 9 tens, leaving 8 tens. 1 ten added 
— tothe 1 unit makes 11 units. 6 units from 11 units 
3 leave 5 units. We write the 5 in units’ place be- 
low the line. 3 tens from 8 tens leave 5 tens. We write 
the 5 in tens’ place below the line. 


91 73 45 Dlieee cs net YOieky OOo LOL OU 

26 38 28 AM SPUR AS £4 ahs Ou Ar Mme: Ae as 1 oe 
2 
2 


95 100 66 SOT eal le G0. os 
37 25 17 SOe rT Cotte (rer lae 106 m2 
98 ~° 64 83 Peeey To Rit Sora Ae), The AG 
45 28 29 25 PHS 68 Be 86 B80 AR 


1. A peach orchard yielded 95 bushels of peaches. 68 
bushels were sold. How many bushels were not sold ? 

2. In a school there were 87 pupils. 49 were boys. 
How many were girls ? 

3. A man had $75. He paid $41 for a bicycle and $18 
for a suit of clothes. How many dollars had he left ? 

4. There are 27 sheep in one pen and 22 in another. 
How many sheep in both pens? 19 of them were sold. 
How many sheep were left ? 


ORAL TEACHING 86 
ANSWER 


FRACTIONS 


>> o> $ zo Ze are fractions. So also are , 2, #, 2, 

3, o) & & & & 10 10 10 10 10 10° 17 10° Read these. 

When fractions are written in figures, the number below 

the line tells into how many parts the thing is divided, 

and the number above the line tells how many parts we 

are talking about. °%, means that there are 12 equal 
parts, and we are taking 5 of them. 


ESTRELLA a 


Point out halves and quarters. 


ae a 


Point out fifths and tenths. 


Point out thirds and sixths. 


el CO 


Point out halves, quarters and eighths. — 


CS an I 


Point out halves, thirds, fourths and twelfths. 


Point out sevenths. 


ee nn a er 


Point out thirds and ninths. 


RN EE FR 


Point out twentieths, tenths and, fifths. 


1. Draw on the blackboard forms of figures showing 
halves, thirds, quarters, fifths, sixths, sevenths, eighths, 
ninths, tenths, twelfths, twentieths, and fortieths. 

2. Tell why the larger the number of parts of anything 
the smaller each part is. 


rie eee 1a aol 1 1 eee et 19 19 
+) What is 3 of 4 4 of 4 of 4 x of 4 4 of +! 
1 pL ee “bepe) Coal AOR Fall aes ah 1 aes aby. 
4 of 4? 4 of 4 of 4? +4 of 4 x of 3 4 of 3% 
1 95 1 39 2 eye 19? 
4 of 2: + Of Bt 2 of 3 2 of 


4. Fold or cut paper to show the facts on this page. 


Q7 STUDY 
ANSWER 


FRACTIONS 


The equal parts of numbers are called fractions. 

Fold or cut paper to show these facts. 

1. 3 of 6=8. Six halves are three wholes or units, 
because two halves equal one whole, and six are three 
times two. §=3. fof6=3 4x6=$=83. 

2 FOLS=s. $=>4. J ors=—4. 4x8=4. 

3. dof 6=§. Six thirds are two wholes, or units, 
because three thirds eines one whole, and six are two 


times three. § = 2. 4 of 6 = 2. 4 bie oi vi 
1 unt aes 1 fe 1 Ae 
4 t+o0of9=}2. 2=3. RUC Ie. weet) Ooo. 
=e ity ea 6.) 4 0f112 ="? 7. of 14=? 
8. of l6=? rere Ul Laie lo. dof 1lb6=? 
v1: tof 18 =? ab 4 of 21 ? 
13. 2 of 9 2x 9= 418 because 9 times two thirds 
are 18 Pigie 18 = 6, eee 18 +3 = 6. 
2 ey ae oe 
um foliam? gxBaae—s COO 
1 1 rads wu 
15. fof8=? }x8=§=2 ae] 
16. Find # of 8, #o0f 12, 20f 16, Coot 
q of 20. Count and see 


17. Find 2 of 10, 2 of 15, 2 of 20, 2 of 25. 

1s. Find 2 of 15, 4 of 20, 3 of 80, 2 of 40. 

19. What: Breage Diy LB e102? 562 97.210? 2247 
20? +30? 

20. Find 4 of 20, 10, 15, 5, 25, 30, 35, 40. 

21. Find 2, 4, and $ of 18, 6, 12, 24, 30, 36, 42, 48. 

22. Find 2, 32, 4, 2, ney, & of 14, 7, 21, 28. 

23. ‘ What are 2, 3, 4, 3, $, and { of 16, 8, 24, 32, 40? 


enloo enh 


ORAL 88 


QUESTIONS 


1. If a bushel of corn cost 80%, what will 8 quarts 
cost? What will a peck cost ? 

2. If a quart of onions cost 9%, how many cents will 3 
quarts cost ? 

3. How many dimes equal 90¢? 

4. A man bought 2 rugs at $9 apiece. What change 
should he get back, if he gave the clerk a twenty-dollar 
bill ? 

5. 45¢ was divided equally among 9 children. How 
many cents did each child get ? 

6. In 2 hours Fred can ride 30 miles on his wheel. 
How many miles can he ride in 1 hour? in 3 hours? 

7. In a school of 84 children there were 12 over 9 
years of age. How many children were under 9 years ? 
What fraction tells the number of children over 9 years 
old ? 

8. Mr. Brown put into his pocketbook 6 ten-dollar 
bills, 3 five-dollar bills, and 4 two-dollar bills. How many 
dollars did he put into the pocketbook ? 

9. What is the ratio of 10.to 5? 

1o. If 5 oranges cost 20%, how many cents will 10 
oranges cost ? 

11. What is the ratio of 6 to 2? 

12. If 2 pencils cost 8%, what will 6 pencils cost ? 

13. Henry has 60¢ in nickels. How many car rides 
can he take at 5¢ a ride? 

14. A baker sold 12 loaves of bread a 4% a loaf and a 
dozen of cookies for 8¢. How much money did he get ? 

15. Emma bought 3 paper dolls for 10¢, and Laura 
bought 2 skeins of thread for a nickel. How many cents 
did both girls spend ? 


89 ORAL 


QUESTIONS 
1. Zof 8=? of 8=? Lof2W=? of 20=? 
Lof44=? 2o0f44=? Lof28=? of 28=? 


One half equals how many fourths ? 
What is the ratio of 4 to 28? of 28 to 4? 
Compare 4 with 36. 4 is } of 36. Hence the ratio 
of 4 os 36 is?. What is the site of 36 to 4? 
5. What is the ratio of 24 to 4? of 24 to 6? of 24 to 12? 
6. Give the ratio of 4 to: 
Sipe, ow 40). 48) 44. 694. 20. 12, 4. 


7. Give the ratio of each of those numbers to 4. 


oN 


s. Ifa hat costs $4, what will a dozen hats cost ? 
9. Divide 24 pears equally among 6 boys. How many 
pears will each boy get ? 
10. There were 2 dozen eggs in a basket. One third 
of them were used for breakfast. How many were left ? 
11. James had 28%. He spent } of his money. How 
many cents had he left ? 
12. 3 tops cost 18%. What was the price of one top ? 
13. Eddie bought 9 apples at 2¢ each. How many 
cents did he pay for them ? 
14. Katie got 4 spools of thread at 3¢ apiece. How 
many cents did she pay for the 4 spools ? 
15. George has 3 nickels. How many cents has he? 
16. Alice had 14 cherries. She gave 4 of them to Lucy. 
How many cherries did Lucy get ? 
17. It is 18 miles from Brooklyn to Garden City. I 
walked } of that distance. How many miles did I walk ? 
How re miles would be ? of the distance ? 


ORAL } 90 
WRITTEN 


QUESTIONS 


1. How many pints are there in + of 6 gallons? 
2. If syrup is 80% a ee hae many cents must be 
paid for a pint? 
3. What is the ratio of 2 to 6? 2 is what part of 6? 
4. If 6 boxes of candy weigh 3 pounds, what will 
2 boxes weigh ? 
5. What will 12 yards of cloth cost at $4 a yard? 
6. When 8 pounds of sugar cost 40 ¢, 1 pound of sugar 
will cost 4 of 40 ¢, or 
Zs What j is the ratio of 18 to 6? of 24 to 8? 
8s. When 7 yards of silk cost $21, a yard will cost + of 
$21, or dollars. 4 yards will cost 4 x dollars, 
or dollars. | 
9. If 9 bushels of apples cost $18, 1 bushel will cost 
4 of $18, or dollars. 4 bushels will cost 4 x 
dollars. 
10. If a dozen oranges cost 60%, what will be the cost 
of 1 orange? of 3 oranges ? of 5 oranges ? 
11. When 5 pounds of meat cost 45%, what will 1 pound 
cost ? 2 pounds ? 
12. When 5 quarts of milk cost 35%, what will 2 quarts 
cost ? 
13. If 4 lemons cost 8%, what will 1 lemon cost? 
2 lemons? What will a dozen lemons cost? A _ half 
dozen ? 
14. If a newspaper costs 2%, how many cents will 7 
newspapers cost ? 
15. A man had 18 oranges. He divided them equally 
among 6 children. How many oranges did each child 
receive ? 


91 


TELLING LENGTHS 


12 inches make 1 foot. 
Lorine > Tt 


in. stands for inch or inches. ft. stands for 
foot or feet. 
3 feet make 1 yard. 
Dive teva. 


Be sure to place a period after in. for inch, 
ft. for foot, and yd. for yard. 

A. foot-rule shows twelve inches. 

A yard-stick shows three feet. 

A foot is a very common unit of measure. 
We buy boards at the lumber yard by the foot. 

A yard is almost as common a unit of measure. 
We buy goods for dresses and suits by the yard. 

An inch is the unit of measure for small 
things. We tell how wide and how long a 
photograph is by inches. 

1. Measure 2 inches on a piece of paper with 
a ruler. 

2. Cut squares 2 inches on each side. 


3. Measure the size of the first picture in this 
book. 

4. What is the size of your desk? Your 
teacher’s desk ? 

5. Ask your mother how many yards of 
cloth she needs to make a dress. Measure that 
number of yards on the blackboard. 


Size means, How long is it? and, How 
wide is it? sometimes also, How thick is it ? 


STUDY 


INCHES 


FIVE 


ORAL 99 


QUESTIONS 


1. A bushel basket is half full of potatoes. How 
many more pecks of potatoes will it hold? 

2. How many quarts are there in a bushel of chest- 
nuts? in a bushel of corn? in a bushel of apples ? 

3. Ifa bushel of wheat weighs 60 pounds, how many 
pounds does a peck of wheat weigh ? 

4. 8 quarts are what part of a bushel? 2 pecks make 
what part of a bushel ? 

5. If 2 bushels of apples cost four dollars, what will 
2 pecks cost ? 

6. How many bushels are there in 64 quarts ? 

7. How many bushels are there in 72 quarts ? 

8s. Arthur gathered half a bushel of chestnuts. To 
how many boys can he give a quart each, after he has 
sold a peck of the nuts? 

9. How many quarts are there in a bushel? in half a 
bushel? How many quarts are there in a quarter of a 
bushel? How many quarts in 2 quarters of a bushel? in 
? of a bushel ? 

10. If you had } of a bushel of berries, how many 
quarts would you have? 

11. Ifa pint of walnuts costs 6 cents, what will 4 quarts 
cost? What will half a peck cost ? 

12. A dish holds 8 pints of berries. How many quarts 
will 6 such dishes hold ? 

13. At 9%aqt., what will a pk. of cranberries cost ? 

14. At 5 cents a quart, what will 1 peck of beans cost ? 

15. How many pecks are there in 9 bushels? in 6 
bushels? in 3 bushels? in 5 bushels ? 


93 ORAL 


REVIEW 


What are # of 18? 2? 4? $8? §? 2? 

What part of Vis 1? Bof 9=? of 10=? 

fy otlO=? dof 20=? {of B=? |, of 100=—? 
A string was 12 yds. 1 ft. long. 2 yds. 1 ft. were 
cut off. How many yards were left ? how many feet ? 


aie od LU os 


5. A tank contained 38 gallons of water. 62 gallons 
more were poured in. Then 47 gallons were pumped out. 
How many gallons were left ? 

6. A milkman has 7 cans, each holding 12 gallons of 
milk. He sells 48 gallons. How many gallons has he left? 

7. James earned 40¢ in one week, and Arthur earned 
55¢. How many cents did both boys earn ? 

8. If James spent 29%, and Arthur spent 36%, how 
many cents did each boy have left ? 


9. A man having $56 bought a suit of clothes for $28. 
What part of his money did he spend? How many dol- 
lars did he have left ? 

1o. At 6¢ a quart, how much money will 6 pints of 
milk cost? 9 pints? 38 gallons? 

11. At 4% a pint, how many pints of berries can you 
buy for 20%? for 80¢ 

12. How many inches long is your shoe? How long 
are your skates ? 

13. How many feet or inches wide is the ring you use 
for marbles ? 

14. If a bushel of peaches costs four dollars, how much 
will a peck cost ? 

15. What will a bushel of potatoes cost at 20% a peck ? 


STUDY 94 
ANSWER 


QUESTIONS 


1. How many ee are there in a quarter of a yard? 
3 of a yard? in 4 of a yard? 

2. Harriet peeant a yard of ribbon. and divided it 
equally, for dress trimming, among her six dolls. How 
many inches of ribbon did she cut off for each doll ? 

3. If you drew a line a foot long and divided it into 12 
equal parts, what would be the name of any of those parts ? 

4. George drew a triangle that was } of a foot on each 
side. How many inches was it around the triangle ? 

5. How many inches are there in 2 of a foot? 

6. How many inches is it Rae a desk top 2 feet 
long and 18 inches wide ? 

7. A ribbon was 3 feet in length. How many inches 
long was it? 

8. If it takes 7 yards of lace to trim a dress, how many 
yards will it take to trim 9 dresses ? 

9. A log of walnut was 30 feet long, 4 of it was cut 
off. How many feet were cut off ? 

10. Mrs. Smith bought 10 yards of silk at $1 a yard. 
She used 3 of the silk. How many yards were left? 
What was the value of the piece of silk she used ? 

11. A bench is 12 feet long and 16 feet wide. How 
many yards is it half way around the bench ? 

12. How many feet are there in 28 inches? How many 
inches over ? 

13. A square room has sides 5 yards and 1 foot long. 
How many feet is it around the room ? 


14. A string 1 foot long is to be cut into inch pieces. 
How many times must it be cut ? 


95 STUDY 
ANSWER 


QUESTIONS 


1. Draw a rectangle 2 inches wide and 4 inches long. 
Divide it into 1l-inch squares. How many squares are 
there in the oblong ? 

2. A room is 3 yards and 1 foot wide. How many 
steps will a boy take in crossing the room if he steps 
2 feet at each step ? 


3. Measure the distance between 2 windows in your 
room. Measure the length and the width of the room. 


4. Inaroom the distance between a door and a window 
was measured and found to be 3 yards and 1 foot. How 
many feet were there in that distance ? 


5. Louise bought a roll of braid, and, on measuring it, 
found that there were 9 feet in the roll. How many yards 
were there in it ? 

6. Mrs. Smith bought 9 yards of silk. She used } 
of it. How many feet were in the piece she used ? 


7. Draw a square with sides 5 inches long. Mark the 
inches on its sides. Divide the square into 9 smaller squares. 


8. Draw a rectangle 1 inch wide and 4 inches long. 
How many 1-inch squares can you make in it ? 


9. On the board make 2 dots, 1 foot apart, guessing 
the distance. Measure the distance between the dots. 


1o. Judge a distance of 1 yard, making the distance by 
putting 2 dots on the board. Measure the distance guessed. 


11. Draw a line that you think is 3 inches long. Meas- 
ure it. 

12. Draw a square that you judge to be 3 of a foot in 
length. Measure the square. 


ORAL TEACHING 96 
STUDY 


HUNDREDS 


We call ten tens one hundred. 

LOSS OF 314) 99 + 1= 100 50 + 50 = 100 

We write one hundred in figures, |OQO. We put the 
1 in hundreds’ place by setting two zeros, 00, at the right 
to show that the 1 is neither in units’ place nor in tens’ 


place. 
We call twenty tens two hundred, and write two hun- 
dred in figures with a 2 in hundreds’ place. 


1004100 = 0'0 20 x 10 = 200 


Two hundred and one hundred are three hundred. 
100 + 100 + 100 = 300 200 + 100 = 300 


Four hundred, 400. Five hundred, SH OKO}. 
Six hundred, b Ores Seven hundred, | OO. 


Eight hundred, SOO. Nine hundred, q OO: 


Above one hundred we count units and tens as we do 
below one hundred. 


We write one hundred eleven in figures, | | |. 


We write six hundred ninety-two in figures, b q oe 


1. 90+11=101. 11=10+1. Nine tens and one 
ten make ten tens. ‘Ten tens are one hundred. The unit 
we set in units’ place. 

2. 844+ 20=104. 84=80+4. Eight tens and two 
tens make ten tens. ‘Ten tens are one hundred. The 
four we set in units’ place. 

3. 70:.4+42=112. 42= 30+ 104 2. 


bo © 


tee fe Wael cr re ered se. MS. oo: be 


(Se) 
bo -1 


OC) pa IND 


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GN ONE aarp PO 


(otek Bes 
> (wen o& 


pet eet DD 
Oost Qe Os 


ADDITION 
36 28 
17 iL 
a 34 
44 ab 

6 22 
yy 38 
18 31 
hed 48 
BIT 
14 24 
24 16 
14 12 
ie 
26 Ie 
10 aa 
19 AA) 
yh at 

2 1 
66 31 
10 Lis 

5 14 

3 27 
10 
16 26 
1s 9 

5 30 

2 Be 
2B 10 


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Aba toe ey ee 
bo CO © Se tm co <¢ 


ae 
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Co ee ee Re CO |] CO 


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WRITTEN 


ORAL TEACHING 98 
STUDY 


METAL MONEY 


Size of a 
quarter 
dollar. 


Size of a Size of a 


dollar. half dollar. 


Size of Size of a Size of a 
a dime. nickel. penny. 


One dollar is equal to one hundred pennies, or cents. 

$ is the sign for one dollar, or 100 cents. 

A half dollar is half 100 cents, or 50 cents. 

A dime is one tenth of one dollar. 100 + 10 = 10. 

A dime is worth ten pennies. 

A quarter dollar is equal to a fourth, or quarter, of 100 
cents, or 25 cents. # is the sign for cents. 

The coins for dollars, half dollars, quarter dollars, and dimes are 


made of nearly pure silver metal by Our Country. ‘That is one im- 
portant thing Our Country, whose flag we know so well, does for us. 


A nickel is equal to five pennies, or 5%. 
The penny is one cent, one hundredth part of one dollar. 
$1 = 100¢. 100¢ + 100 = 1c. = one penny. 


Nickels are made of nickel metal. Pennies are made of copper. 


99 ANSWER 


NUMBER-STORIES 


1. Mary and Tom are at the grocery. They have three 
quarters to spend. Mother wishes them to ask the grocer 
for three pounds of sugar, half a pound of tea, and a dozen 
egos. Mr. Grocerman tells them that sugar is five cents 
a pound, tea is forty cents a pound, and eggs are twenty- 
five cents a dozen. ‘Tom will carry the things home in the 
basket. Why does the grocer weigh the sugar? When 
Mary takes the “change,” or money he gives back to her 
with the packages and the eggs, how many cents does she 
have to take home to mother ? 

3 quarters = three 25¢ pieces of silver. 8 x 25¢=Td#. 

3 pounds of sugar at 5¢ a pound cost three times 5f. 
8x bf =15¢. 

1 pound of tea at 40% a pound costs one half of 40%. 
4 of 40¢=20¢. The eggs cost 25%. 

15+ 20¢425f=60f T5¢—60f=15¢ 
Mary has fifteen cents to take back to her mother. 
Do you see now why we have to learn about numbers ? 


2. Tell a number-story about Charlie and Susan. They 
have fifty cents. They wish to buy two pounds of sugar 
at five cents a pound, a loaf of bread at eight cents, and a 
pound of butter at twenty-eight cents. How much will 
they have left ? 


3. Make up a story about Willie and Jennie, who have 
one hundred cents. ‘They ask Mr. Grocerman for half a 
dozen eggs, two pounds of butter, and three large loaves 
of bread. He asks them twenty-eight cents a dozen for 
his very best eggs and twenty-eight cents a pound for 
table butter and ten cents for large loaves of bread. They 
gave him a silver dollar. Was this right ? 


WRITTEN 100 


QUESTIONS 


1. What is the ratio of 12 to6? of 6to12? of 36 to 6? 
of 24 to 6? of 72to6? of 48 to 6? of 54 to 6? of 18 to 6? 
of 30 to6? of 42 to6? of 6to18? of 6 to 24? of 6 to 42? 
of 6 to 86? of 6 to 48? of 6 to 54? of 6 to 72? 

2. If 6 dozen apples cost 72%, how many cents will 1 
dozen cost ? 

3. How many minutes past the hour is it when the 
minute hand points to III? 15 minutes are what part of 
an hour? 80 minutes are what part of an hour ? 

4. A farm of 72 acres is one sixth woodland. How 
many acres are woodland ? 

5. A table is 48 inches long and 36 inches wide. How 
many inches is it around the table ? 

6. What will 6 apples cost, if 4 dozen cost 96¢? 

7. The price of a sofa was $66. It was reduced } in 
price and was then sold. What was the selling price ? 

s. A woman had 5 ten-dollar bills and 3 two-dollar 
bills. She bought 8 yards of velvet at $6 a yard and 1 
yard of silk for $3. How many dollars did she spend ? 
How many dollars did she have left ? 

9. A grocer paid $60 for 30 barrels of apples. What 
was the cost a barrel? He sold the apples for $90. How 
much did he get a barrel? How much did he gain on 
each barrel? How much did he gain on the 30 barrels? 

10. A pail holds 12 quarts. How much will it cost to 
fill it with milk at 6% a quart? After 4 of the milk is 
used, how many pints are left ? | 

11. In one day Mr. Smith rode 80 miles on his wheel. 
He rode 4 of the distance in half an hour. How many 
miles did he ride in that time ? 


aaa 


101 


ORAL TEACHING 
STUDY 


READING AND WRITING HUNDREDS 


thc Ll 
ke Hes 
ep Te Pp 
400 900 
50 8 0 

1 7 
451 987 


n mM 

uo) 4°. 

2 
Sm Q Sa 
EES EES 
map Hap 
700 4 0 0 
T 0 2 0 
T 2 
(per he di 422 


1. Read the numbers: 299, 648, 110, 444, 770, 801, 999. 


2. How many more hundreds has 897 than 153? how 
many more tens has 897? how many more units ? 


3. Tell how many hundreds, how many tens, and how 
many units there are in: 


393 406 744 985 112 
615 600 401 642 371 
350 404 199 878 555 
611 225 111 226 414 
660 218 922 660 882 


630 808 299 681 
TO00 400" OO 1P ae Li 
Suz oto" "60s “187g 
901 584 T17 205 
961 3821 201 


4. Write by figures: 
One hundred twenty-five. 
One hundred ninety-nine. 
One hundred six. 

Two hundred forty-six. 
Two hundred eighteen. 
Two hundred two. 
Three hundred eleven. 
Three hundred thirteen. 


Four hundred twenty-eight. 


Four hundred eighty-one. 
Four hundred ninety. 


1000 


Five hundred five. 

Five hundred fifty-five. 
Six hundred ninety. 

Six hundred eight. 

Seven hundred seventeen. 
Seven hundred seven. 
Eight hundred forty-eight. 
Eight hundred thirty-six. 
Nine hundred twenty-one. 
Nine hundred fifty. 

Nine hundred ninety-one. 


ORAL 


102 


REVIEW OF HUNDREDS 


1. Write these numbers in figures: 7 hundreds. 7 hun- 
3 hundreds 6 tens 7 units. 4 hun- 


dreds 2 tens 8 units. 
dreds 1 ten 1 unit. 
1 hundred 4 tens 3 units. 
4 units. 9 hundreds 8 tens 6 units. 


3 tens 2 units. 


6 hundreds 5 tens 2 units. 


2. 220=1104? 


425 = 200+? 
630 = 220 + ? 
530 = 130+ ? 
840 = 235 4+ ? 


545 = 140+? 
250 = 404? 
610 + ? = 820 
115 + ? = 720 
200 + ? = 325 


8 hundreds 5 tens 5 units. 2 hundreds 
5 hundreds 7 tens 
3 hundreds 1 unit. 


725 + ? = 930 
525 + ? = 835 
330 + ? = 640 
835 + ? = 940 
T49 + ? = 957 


3. How many 10’s are there in 200? 300? 400? 500? 
600? 700? 800? 900? 1000? 


2 tens X0=? 
betens Xf 
o tensx5o=? 
8 x 6 tens=? 
4 tens x 8=? 


6 tens x 6=? 


Dj Xen bee 14 
4x4 tens=? 
0 Tense." 
oetons <= — 
6 tens x 6=? 


7 tens xX 2=? 


2 tens x 6=? 
4 tens x 4=? 
5x 5d tens=? 


3x9 tens =? 


-8 tensx 4=? 


7x2 tens=? 


4. How many figures are needed to express units, or 
ones ? to express tens? to express hundreds ? 


5. Write a 10’s Table to 1000, in ten parts, 1 to 100, 
101 to 200, 201 to 300, 301 to 400, 401 to 500, 501 to 600, 
601 to 700, 701 to 800, 801 to 900, 901 to 1000. 


103 ORAL 
WRITTEN 


HOUSE NUMBERS 


In towns and cities the streets are named, and the houses 
and lots on the streets are numbered. One side of the 
street has odd numbers, and the other side has even num- 
bers. If there is room between houses for more houses, 
then these lots, sometimes called vacant lots, are numbered. 

Has your house a number, and your street a name ? 

If you live in the open country where there is plenty of 
room, and people do not need names for their roads and 
numbers for their houses, probably you know where some 
townspeople have their houses or stores. 

The name of the street and the number of the house are 
part of the address. Mr. William Jones, 165 Main Street. 

Sometimes when there are very many streets, the streets 
have numbers for names. When we wish to write a letter 
to a person living in a different place from our own town 
or city, we write on the envelope what the place is where 
we wish the letter to go. 


Master Charles Marshall, 
149 Sixth Street, 
Atlanta, 
Georgia. 
If houses were not numbered in large towns and cities, 
it would take a great deal of time to find people in them. 
1. Write your house address or that of some friend. 


2. Exchange your paper with its address for that of the 
boy or girl in front of or behind you. Read that, and 
copy it. Exchange across the aisle. 


3. Has your schoolhouse any address? 


4. Where is your town or city hall? Your post office? 


ORAL TEACHING 104 
STUDY 


THOUSANDS 


We call ten hundreds thousands. 
10 x 100 = 1000 999 + 1 = 1000 500 + 500 = 1000 


We write one thousand in figures, |OOQ. We put 
the 1 in thousands’ place by setting three zeros, 000, at the 
right to show that the 1 is neither in units’ place nor in 
tens’ place nor in hundreds’ place. 

We call twenty hundreds two thousand; and write two 
thousand in figures with a 2 in thousands’ place. 


1000 + 1000 = 2000 20 x 100 = 2000 
Two thousand and one thousand are three thousand. 
1000 + 1000 + 1000 = 3000 2000 + 1000 = 3000 


We write four thousand HOOO, five thousand 


50 0 0, six thousand bO O O, seven thousand | OO,03 
eight thousand 6 O O 0, nine thousand dO 00. 


Ten tens we call one hundred. Ten hundreds we call 
one thousand. Ten thousands we call ten thousands. One 
hundred thousand we call one hundred thousand. 

We write one hundred |QQ. We may write one thou- 
sand!|QQOQO. The comma is to help us see that there are 
3 zeros, and to read thousands quickly. We write ten 
thousand |QOQOQQO. We write one hundred thousand 
|OOOOO. It is not necessary to use a comma. 

1. 900+ 101 =1001. 101=100+4+ 1. Nine hundreds 
and one hundred are ten hundreds or one thousand. 

2. 700 +420= 1120. 420=300+120. Seven hun- 
dreds and three hundreds are one thousand. ‘The twelve 
tens we write as one hundred twenty. 


105 STUDY 
ANSWER 


THOUSANDS 


1. One thousand one, 1001. One thousand nine, 1009. 
One thousand ten, 1010. One thousand eighteen, 1018. 
One thousand one hundred eighteen, 1118. 

Two thousand seven hundred four, 2704. 

Three thousand thirty-six, 3036. 

Five thousand six hundred sixty, 5660. 

Seven thousand seven hundred seventy-seven, T7777. 

Eight thousand one hundred one, 8101. 

Eight thousand eight hundred fifteen, 8815. 

Nine thousand four hundred ninety-seven, 9497. 

2. Read: 1246, 9223, 4780, 6111, 4644, 8707, 3136, 
4598, 9610, 7000, 3688, 2080, 6202, 7100, 8004, 9110, 
1338, 9909, 4707, 8118, 7656, 8771, 4919, 7223, 2748, 
4339, 4716, 3188, 7007, 3010. 

3. Write by figures: one thousand two hundred sixteen; 
three thousand seven hundred twenty-eight; nine thou- 
sand four hundred sixty-three; seven thousand seven 
hundred; eight thousand nine hundred seventy; two 
thousand seventy-five ; four thousand four; six thousand 
six hundred sixty-six; nine thousand ten; eight thousand ; 
three thousand one hundred forty-four; five thousand 
eight hundred eighty-one. 

4. Write in words: 7414, 38602, 8435, 1014, 5005, 2110, 
6116, 9711, 4419, 2829, 1990, 3333, 5208. 

5. Give the number of thousands, of tens, and of ones 
in each of the numbers in 2 and 4. 


6. Count by hundreds from 1000 to 2000. 
7. Count by thousands from 2000 to 9000. 


8. What is the greatest number that can be expressed 
by three figures? by four figures ? 


ORAL TEACHING 
STUDY 


106 


FIVES AND TENS 
5 10 15 20 25 30 35 40 45 50 55 60 


04+5= 5 5+5= 10 10+5=15 
15+ 5= 20 20 + 5 = 25 25 + 5 = 80 
380 +5 = 30 35 +5 = 40 40 +5= 45 
45+5=50 50 +5 = 55 55 + 5 = 60 


oleae 23 XR) te 
ional) 5x 8=40 
5x38=165 5x 9=45- 
ox4= 20 aim an ANE l0) 
B16) Sys Sy ah Lee aye 


5x 6=30 ox 12=60 


MULTIPLICATION TABLE OF FIVES 


Make a division table, beginning it like this: 


5+5=1 
10+5=2 


ees 


74 | eos 


LO Sol= eb LOS es eee! 


LOK est) 


LOK 930 
10 x 4= 40 
LOS. == D0) 


LOS LO atu 


10x67 60 


LO Sce alte 11) 
LOS 120 


MULTIPLICATION TABLE OF TENS 


107 ORAL TEACHING 
STUDY 


FIFTHS AND TENTHS 


When anything is divided into five equal parts, we call 
each part one fifth. Five fifths make one whole. 


Circle Square Rectangle Pentagon 
Line 
Star Rectangle 


Into how many equal parts is each of these forms divided ? 

1. Point out two fifths of each of these forms; three 
fifths; four fifths. 

2. Make drawings like these forms on paper but larger. 

3. Make drawings lke these forms on the blackboard. 


When anything is divided into tenths, it has ten equal 
parts. Ten tenths make one whole. 


® WII & 


Into how many parts is each of these 
forms divided? Count and show the 
parts. 

Make drawings like these forms both 
on paper and on blackboard. 


ORAL TEACHING 108 
STUDY 


SIXES AND TWELVES 
6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 
0+6= 6 6+6=12 12+6=18 18+ 6= 24 
24+ 6=30 30 + 6 = 86 36+ 6= 42 42+4+6= 48 
48 +6 = 54 o4 + 6 = 60 60 + 6 = 66 66+6= 72 


6x 1 =) 6 
6x2=12 
-6x3=18 


6x4= 24 

656530 

6x 6 = 36 

MULTIPLICATION TABLE OF SIXES 
12 24 36 48 60 72 84 96 108 120 132 144 

O+12= 12 12412= 24 24412= 386 386412= 48 
48+12= 60 60412= 72 72412= 84 84412= 96 
96+12=108 1084+12=120 1204+12=1382 1382412=—144 


Make up bundles of splints, each with twelve splints, 
and show that these facts are true. 


12x%1=12 12x 7= 84 
12% 2=24 12x 8= 96 
ee 12x 9=108 
12x 4=48 12 x 10 = 120 
12x 5 =60 12 x 11 = 132 
12x 6=72 J nosp 44 


MULTIPLICATION TABLE OF TWELVES OR DOZENS 


109 STUDY 
ANSWER 


SIXTHS AND TWELFTHS 


When anything is divided into six equal parts, we call 
the parts sixths. Six sixths make one whole. 


Circle Rectangle Hexagon 


1. Show that each of these forms is divided into halves. 

2. Show that each is divided into thirds; into sixths. 

3. Make larger drawings of each of these forms on 
paper; on the blackboard. 


When anything is divided into twelve equal parts, we 
call the parts twelfths. ‘I’welve twelfths make one whole. 


Circle Rectangle Hexagon 
1. Show the various halves in the circle and: hexagon. 
2. Show thirds of each of these forms. 
3 


Show fourths of each. 4. Show sixths of each. 


5. Make larger drawings of each of these forms on 
paper; on the blackboard. 

6. §=1; 42=1; 3=1; 4=1. Read of these facts. 

7 r4? Why? dor ,? Why? 

8. Cut out forms to show the answers to 6 and to 7. 

9 


Which is larger, 3 or 4? #or4? +#or 4? 


ORAL 110 
WRITTEN 


DIVISION TABLES 


Make a division table, beginning it like this: 
10+10=1/30+10=3 


20 +10 = 2/40 + 


Make a division table, beginning it like this: 
6+ 6=1/18+ 6= 


196 = 2174 


—|— 


Make a division table, beginning it like this : 
12+12=1/86+12=3 
24-+-12=2)48+12= 


QUESTIONS 


1. How many school days are there in 4 weeks? How 
many working days ? 

2. How many hours are there in a quarter of a day ? 

3. Which is the greater fraction, } or }? 

4. A cake is cut into sevenths. Another cake of equal 
size is cut into tenths. Would one of these sevenths be a 
larger or smaller piece of cake than a tenth ? 

5. How many 10’s are there in 96? how many units ? 

6. If a can of peaches cost 25%, how many cans will 
$1 buy? T5¢? 

7. What is the ratio of 6 to 48? 

s. If 2 yards of tape cost 24%, what will 1 yard cost? 
what will } of a yard cost ? 

9. A strip of carpeting is ? of a yard wide. How 
many inches wide is the carpeting ? 


Tt ORAL 
WRITTEN 


QUESTIONS 


1. If you had a fifty-cent piece, a dime, and 2 nickels, 
how many cents would you have? How many more cents 
would you need to make a dollar ? 

2. A dealer paid $96 a dozen for lamps. What was 
the cost of 1 lamp ? 

3. A girl bought 8 yd. of braid at 6f a yd. She gave 
the clerk a 50% coin. What change should she get ? 

4. How many nickels are equal to 40¢? 

5. How many cents are there in a dollar ? 

6. If a blank book cost 7%, how many blank books can 
you buy with 3 dimes? How many cents would you have 
left after paying for the books ? 

7. Louis bought half a dozen little flags at 12¢ apiece. 
He gave the clerk a half dollar and a silver quarter. What 
change should the clerk give Louis? 

s. A boy works in a garden at 10¢ an hour. How 
many hours must he work in order to earn $1? 

9. What is the ratio of 6 to 12? of 9 to 27? 

1o. If a dozen oranges cost 50%, how much will half 
a dozen cost ? two dozen ? 

11. A man bought a pound of cheese for 15%. He ate 
4 of it. What was the value of the part he ate ? 

12. At $6 a ton, how many tons of coal can you buy for 
$27? What will half a ton cost ? 

13. What is the ratio of 18 to 36? of 36 to 18? 

14. If 36 crates of peaches cost $40, what will 18 crates 
cost? How many crates would $80 buy ? 

15. Mrs. Brown bought 9 yards of sheeting at 7% a 
yard and 3 yards of calico at 5¢ a yard. She gave the 
clerk a dollar bill. What change should she get ? 


STUDY 112 
ANSWER 


REVIEW ; 


1. 700+420=1120. 420=4004+20. Seven hundred 
and four hundred are eleven hundred. We write twenty 
in tens’ place. 

2. Add: 950 800. 700 -800 900 850 880 990 

100 250 600 750 950 600 900 400 


3. Write in figures two thousand three hundred fifty- 
six, four thousand nine hundred ninety, six thousand two 
hundred sixty-two, eight thousand eight hundred. 


4. Which is larger; 4, or 4? <3 or #?. 38.07 


# or¢? Show the answers by drawing forms. 

5. Can you tell which is larger, one tenth or one 
twentieth of anything? Do you see that equal parts 
grow smaller as the number-names grow higher? Ten 
is higher than four, but one tenth is smaller than one 


fourth. Why? 


lly aie dl 1 df Weande 
6. Compare 4 and+by drawings. and 4%. 4 and +5 


7. Compare 2 and #. How much larger is the ?? 
Show your answer by a rectangle divided into twelfths. 

s. What is the ratio of 8to 16? of 12 to 24? 

9. If 16 pounds of oatmeal cost 40%, what will 8 


pounds cost? 12 pounds? 


enleo 
aw) 


10. Mr. Brown bought 4 dozen pears. 38 of the pears 
were bad. ‘The goods ones were divided equally among 9 
children. How many pears did each child get ? 

11. From a door to a window the distance is 2 yards 
and 1 foot. How many feet is the distance ? 

12. Carrie bought a yard and a quarter of red ribbon 
and # of a yard of white ribbon. How many yards in all 
did she buy ? 


113 _ WRITTEN 
QUESTIONS 


1. Divide each of these numbers by 6, by 3, and by 2: 
18, 12, 42, 36, 54, 48, 6, 84, 96, 72, 24, 60, 30, 66, 90, 78. 
2. Find 4, 2, 3, 4, and g of each of the following 
numbers: 60, 30, 86, 72, 18, 54, 48, 42, 24, 84, 96. 
3. 2 of 30=? 43 of 80=? Then 2=what other 
fraction? Show by a drawing. 
4.2 of 18=? 42 of 18=? Then 2= what other 
fraction? Show by a drawing. 
5 fof 12=? go0f12=? Jof12=? sof 12=? 
Then 3? = what other fraction ? 
6. How many sixths of a number equal one third of 
the number? How many sixths equal one half ? 
7. How many fourths and sixths are in two ? 
SB tof18=? 4of18=? go0f18=? 4 of 18=? 
9. ‘Two thirds of 18 equal how many sixths of 18 ? 
10. Two thirds of 30 equal how many sixths of 30? 
11. dof 24=? 2o0f 24=? One half of 24 equals how 
many sixths of 24? 
12. 2 of 836=? 4 of 836=? How many thirds of 36 
equal four sixths of 36? 
13. One half of 24 equals how many sixths of 48 ? 
14. One third of 42 equals how many sixths of 42? 
15. One half of 54 equals how many sixths of 54 ? 
16. One third of 54 equals how many sixths of 54? 
17. tof 60=? 2 of 60=? 4 of 60=? 2 of 60=? 


18. Draw illustrations to show @, 2, 4, 3%- 


ORAL TEACHING 114 
STUDY : 


DATES 


There are always seven days in every week. There are 
always at least four weeks or twenty-eight days in every 
month. There are twelve months in every -year. “ A 
hundred years make one century. We are living in the 
twentieth century, because it is more than 1900 years since 
Jesus Christ was born. When we write letters we put 
three facts at the top, called the date. We tell the year, 
the month, and the day of the month: sometimes we tell 
also the day of the week. We may write the date, 


January 1, 1900, or Tuesday, Jan. 1, 1900. The calendar 
tells us how to know the 


‘< = a b> month, the day of the month, 
¢ ¢ £ 8 % & F the year, and the day of tl 
ok me ak Re errs year, and the day or the 
ee les er eed exer week. 

| 

LZ | 3 lt PLO OTe This calendar is true for any 
| | ——|——_|_} month when the first day of the 
8 | 9 10) 11) 12/13/14 month falls on Sunday and when 
ror oF wi the month has 31 days. This 
15 16 | 17,18 19) 20) 21 calendar represents December, 
| 1901, and March, 1903. If the 
a ea ae feos He 31st day were omitted, it would 
represent June, 1902, and No- 

The Pete pee vember, 1903, also. 


The names of the months are: January, February, 
March, April, May, June, July, August, September, 
October, November, December. 


The year has 865 days, except “leap year,” which has 
366 days. Leap year comes every four years ; then Feb- 


ruary gains another day. 


Thirty days hath September, Until the year 2400 every 
April, June, and November, year we can divide by 4 will 
All the rest have thirty-one, be leap year. We usually call 
Excepting February alone. thirty days a month unless 
Twenty-eight are all its store we know the exact month in 


Till leap year gives it one day more. question. 


115 ORAL TEACHING 
ANSWER 


THE CALENDAR 


1. Get a calendar for the present year. On what week 
day did the first day of this month fall? On what week 
day will the first days of all the rest of the months of the 
year fall? On what week day did the first days of the 
past months fall ? 

2. Can you find what months of each year usually have 
the same days of the months on the same days of the week ? 
Why is this not true in leap year ? | 

3. ‘Tell the names of the longest months. 


4. How many days are there in seven weeks? in three 
weeks ? in eleven weeks ? 

5. How many weeks are there in thirty-five days? in 
forty-nine days? in eighty-four days ? 

6. Which is the longer time, six weeks or two months ? 
ten weeks or three months? one hundred days or three 
months ? 

7. Make a rectangle upon a sheet of paper seven inches 
long, five inches high. Mark the inch spaces on it on 
each side. Draw lines across and up and down so as to 
make thirty-five squares, one inch on each side. 

8. Cut out thirty-one squares; number them from 1 
to 31. 

9. Place these squares on the sheet of paper to show the 
present month. Write at the top of the calendar, § for 
Sunday, M for Monday, T for Tuesday, W for Wednesday, 
T for Thursday, F for Friday, 5 for Saturday. 

10. Make a large monthly calendar on the blackboard. 

11. Make with the squares, as in 1 above, a calendar for 
the next month; the last month. 

12. Make February of this year; of the next leap year. 


ORAL TEACHING 
STUDY 


116 


TELLING TIME 


i) 
Si tit I 


Twenty minutes past 
eight o’clock. 


nly 


There are 24 hours in every day. 
The first hour begins halfway be- 
tween sunset and sunrise, when 
the night is darkest. Wecall the 
end of one day and the beginning 
of the next day midnight. Then 
we count 12 hours, 1, 2, 3, 4, 5, 6, 
(S.ne, LOU (2s herrea 
twelve o'clock in the daytime, it 
is just halfway between sunrise 
and sunset. ‘Then we begin over 
again, and count 1, 2, 3, to 12, 


_when it is midnight again. 


Noon means 12 o’clock in the daytime. 

Midnight means 12 o’clock in the night. 

On the clock face we find Roman figures. 
Ih feyoter es AES aseaeay IB 


Zetwo oll S45 eciotitey ELE 
3 three III 9 nine 
£ fours Elie LO ten 
© five V_ 11 eleven 
Omsk 1V be 12 twelve cll 
Dele 90 oa= NL) 
after V means V+ I. 
fore X means X — I. 
On the clock face we do not 
find any figures to tell us about 


the minutes. 


I be- 


IX 
xX 
XI 


Key to clock face. 


60 minutes make 1 hour. Sign for morning hours, A.M. 
12 hours make 1 half day. Sign for afternoon and even- 


24 hours make 1 day. 


ing hours, P.M. 


Ltt ORAL TEACHING 
STUDY ANSWER 


TELLING TIME 


1 hour o’clock is the same place as 5 min- 
utes. There are two hands on every clock, 
the hour hand and the minute hand. 


The hour hand is always shorter than the minute hand. 


When we studied the fives’ table, we found that 
5 x12=60. There are 60 minutes in every hour, and 
12 hours in every day. 

The hour hand goes from XII to I in one hour, but the 
minute hand goes all the way around from XII past I, 
I], II], and so on to XII every hour. The minute hand 
goes twelve times as fast as the hour hand. 

There are twelve numbers on the clock face to mark 60 
minutes. Each number means in minutes just 5 times as 
much as it does in hours, on the clock. | 


I means in hours 1, but in minutes it means 5, 5x 1=5. 

II means in hours 2, but in minutes it means 10. 

III means in hours 3, but in minutes it means 15. 

IIII means in hours 4, but in minutes it means 20. 

V means in hours 5, but in minutes it means 25. 

VI means in hours 6, but in minutes it means 30. 

VII means in hours 7, but in minutes it means 35. 

When the minute hand points to more than 30, we usually read the 
number of minutes before the next hour. 

6 o’clock and 35 minutes we usually call 25 minutes before 7. 60 


minutes less 35 minutes are 25 minutes. 
Railroads read this time 6 hours 35 minutes. 


VIII means in hours 8, but in minutes it means 40. 


6 hours 40 minutes are twenty minutes before 7 hours. 


IX means in hours 9, but in minutes it means 45. 

X means in hours 10, but in minutes it means 50. 

XI means in hours 11, but in minutes it means 55. 

XII means 12 hours, or 60 minutes, or 0 (no) minutes. 


ORAL TEACHING 118 
ANSWER 


TELLING TIME 
We say, “It is two o'clock.” This means “It is two 


hours of the clock.” When it is 2 o’clock, we find the 
minute hand at XII hours or 60 or 0 minutes. 


2 o'clock 10:20 o'clock 4:45 o'clock 
twenty minutes quarter of 
after ten five o’clock 


This circle is divided into quarters. When the minute 
hand reaches 15 minutes after XII or 60, we say it is quar- 
ter past whatever hour the hour hand 


(| is nearest. A is at III or 15 minutes. 
B A When the minute hand reaches 45 min- 
EY, utes after XII or 15 minutes (60 — 45 
= 15) before XII, we say it is quarter 

one half C one half jefore the hour the hour hand is nearest : 
: : that is, the hour toward which the hour 


hand is traveling. When the minute hand is at VI or 30 
minutes, we say it is half past. 380=60+2. 30=4 of 60. 


1. Where should the hands be to show quarter past 9: 
quarter to 11; half past 9; quarter to 12; quarter past 
10; half past 8; half past 3; half past 7; quarter to 12; 
quarter past 1; quarter ‘past 6; half past 5? 

2. Where is each hand at quarter past 12? at quarter 
past 2? at quarter to 3? at half past 4? at half past 6? 
at quarter to 9? at half past 11? at quarter to 8? at half 
past 3? at 10 minutes after 10 ? 


119 BUSY WORK 


TELLING TIME 


1. Make a large clock face on thick paper or cardboard, 
or on the blackboard. 


2. Draw the hands to show 5 minutes past 9 o’clock, 
10 minutes past 10 o'clock, 15 minutes past 11 o’clock, 20 
minutes past 12 o’clock, 25 minutes past 1 o’clock. 

3. Draw the hands to show 25 minutes of 3 o’clock, 20 
minutes of 4 o’clock, 15 minutes of 5 o’clock, 10 minutes 
of 6 o’clock, 5 minutes of 7 o’clock, and 8 o’clock. 


4. Draw quarter past nine o’clock, half past ten o’clock, 
quarter of eleven o’clock, and six o’clock. 

5. Draw each one of the hours one o’clock, two, three, 
four, five, six, seven, eight, nine, ten, eleven. 

6. Make out of cardboard a clock face, and hands out of 
cardboard or wood, and set the time to suit your own ideas. 
Make all the different times o'clock in 2, 3, 4, and 5 above. 


7. Draw a picture of the clock in your schoolroom. 
What time does it tell? Perhaps it took you quite a long 
time to draw that picture. Draw another, telling what 
time it is now. How many minutes apart are the two 
times on the two clocks ? 

8. School begins at o’clock. Recess is at 
o'clock. Recess is over at o'clock. The morning 
session ends at o'clock. Draw four clock faces to 
show these times. 


9. Do you have a daily program at school? When 
did this lesson begin ? When will it end? Make clock faces 
to show these times. Show the times for other lessons. 

10. Make clock faces showing the time when you get up 
in the morning, when you eat breakfast and other meals, 
and when you go to bed at night. 


ORAL TEACHING 
STUDY 


120 


TELLING HEAT AND COLD 


In the winter, when the fire goes out, we feel cold. 
In the summer we are often very warm. Sometimes in 
winter the fire is very hot, and our rooms are too warm. 


212° Water boils 


200 


° 
150 


100 98 Body warmth 


90° Warm bath 


70° Pleasant heat 
50. 


32° Ice melts 


0° Zero cold 


Fahrenheit thermometer. 
The spaces are called 
degrees. This means 
equal parts of space. 
The sign for degree 
is a 


It is hot near bonfires or the fire in 
the blacksmith’s shop. It is warmer 
in the sunshine than in the shade. 
We call the warmth or coldness of 
the air, the temperature. 

We have thermometers to tell us 
how warm or how cold it is. Ther- 
mometer is from thermo, heat, and 
meter, measure. Inside the glass of 
the thermometer is a liquid heavier 
than water. This is a metal called 
quicksilver or mercury. It looks ike 
silver, but it flows quickly. Did you 
ever see little balls of quicksilver 
run across a table? This quicksilver 
needs more room and goes up the 
tube of the glass, when it is warm, 
but gets smaller and goes down in 
the glass when it is cold. If the 
glass is put in water with broken ice 
in it, the quicksilver goes to 32°. If 
we hold the bulb or thick end tight in 
one hand, the quicksilver goes nearly 
to 98°. In boiling water the quick- 
silver marks 212°. Hot weather is 
when the air is as warm as our bodies, 
Shek 

We like to have the air in our rooms at 70°; 
but in winter, to make the air pleasant at that 
temperature or warmth, we must have water 
vapor in it. That is why we put water on 
our stoves or in our furnaces, or let steam 
out of the steampipes into our rooms. 


Cold air has only a little water vapor in it. 
When we warm the cold air, it needs more 


moisture to make it pleasant to breathe. 


121 ANSWER 


TELLING HEAT AND COLD 


1. How many degrees do you find between melting 
ice and body warmth? 98° — 32° = 

2. How many degrees do you find between melting ice 
and the warm bath? 90° — 32° = 


3. Would you like to go swimming in a river full of 
floating blocks of ice? Why not? 


4. Do you like to drink ice water when warm? Why ? 


5. We like to go swimming in salt sea water at 68°. 
How many degrees is that colder than our bodies ? 


6. In lakes there are often springs of cold water at 
45°. Swimmers often have chills called “cramps” in fresh 
water because of these springs. Why? 98° —45°= 


7. Cool water, 55°, is very pleasant and good to drink 
in summer when our bodies become very warm in the hot 
air. How much cooler is the water than our bodies if our 
temperature is 99° ? 


8. When we are sick, we usually have fever. Over 
100° may be a fever. If our body warmth is 104°, our 
doctor is very anxious. How many degrees too warm is 
this? 104° — 98° = 

9. Sometimes we have a chill. If our body warmth 
falls three degrees, 3°, how warm:are we? 98° —3°= 


10. The temperature inside the mouth is 98° or 99°; 
that of ice cream is usually 32°. Why does it seem so cold? 


11. We warm the air with our body warmth. When 
the wind blows, it takes the warm air away from the skin 
fast. This is why we get just as cold in a strong wind 
when the air is 50° as we do on a quiet day when it is 32°. 
Compare 98° — 50°= and 98° — 82°= 


RATIOS 122 
STUDY 


MUSIC FRACTIONS 


In music we have equal parts or fractions of time. 
A whole note is the musical unit of time. 


oO 18a whole note © © are two whole notes. 
is a half note vie" 4 — 1. 


} isa quarter note 2 , i ie —) nso hale 
a an eighth note © “iPass bol papas = OOK ae 


The space between the two vertical bars in this drawing is one meas- 


ure. One whole note would take 
Ic A. | S | all the time in this measure. 
Two half notes would take all 
the time. ‘T’'wo quarter notes 


and one half note would also take all the time. 


5 » 1. fg +GH5S 1 
i Rae is ti +445 4+g=1 
3. ¢+4= 1. 
Pr eee ee ag Gs tar eae 
5. gg te ao 
ale 


123 ORAL TEACHING 
STUDY 


TELLING ANGLES 


B B 
E F 
C A G 
H G 
D D 


A circle with 4 quarters A circle with 8 eighths 
and 4 right angles. and many different angles. 


> 


AC isa diameter. It divides the circle into halves be- 
cause it is a straight line through the center of the circle. 
BD isa diameter. It divides each of the circle’s halves 
. by pore fal Wo By hy en Pe 
into two equal parts: 4 of $= 


Dee / 


conse Right Obtuse 


These are angles: 


Angles are formed by the meetings of lines. AWB is 
anangle. ‘Trace it. 

Two diameters crossing each other so as to divide a 
circle into quarters make right angles with each other. 

We say that BW is perpendicular to AW because it forms 
the right angle AWB. 

We call angles smaller than right angles acute angles. 
ANE isan acute angle. Point out other acute angles. 

We call angles larger than right angles obtuse angles. 
ANF is an obtuse angle. Point it out. 

We call this a horizontal line : 

And this we call a vertical sae 


ABCD is the perimeter or circumference of the circle. 


ORAL 124 


QUESTIONS 


1. What is the ratio of 5 to 50? of 5 to 5? of 5 to 25? 
of 5 to 40? of 5to 55? of 15 to 5? of 85 to 5? of 45 to 5? 
of 10 to 5? of 20 to 5? 

2. What part of 80 is 5? 6? 12? 18? 24? 

3. A mason can build a wall in 30 days. What part 
of it can he build in 5 days? in 6 days? in 18 days? in 
12 days? in 24 days? 

4. George can ride 50 miles in 5 hours on his wheel. 
What part of that distance can he ride in 1 hour? in 3 
hours ? in 4 hours ? 

5. How many feet are Hie in 25 inches? in 380 
inches? in 60 inches? 

6. Esther bought 9 yards of braid at 5¢ a yard. She 
gave the clerk a fifty-cent piece. What change should 
she get ? 

7. How much money will 5 gallons of kerosene cost 
at 12¢ a gallon? 

8. Walter paid 40¢ for 2 quarts of molasses. How 
much would a pint cost at the same rate ? 

9. At 11¢ a quart, how many quarts of berries can pee 
buy for 55¢? 

10. Mr. Brown wishes to divide 40¢ equally among his 
four children. How many cents must he give to each 
child ? 

11. Ina pond there were 36 lilies. A boy picked 9 of 
them. What part of the whole number of lilies did he 
pick ? 

12. A florist had 44 roses. - of them were white, =4, 
were red, and the rest were eas How many roses ihe 
white? How many were red? How many were yellow? 


ee 


125 BUSY WORK 


REVIEW 


1. With a thermometer take the temperature out of 
doors at 8.80 A.M., at 12M.,and at 8p.m. Tell the differ- 
ences. Do this for five school days. 


2. Take the temperature in the schoolroom every hour 


all day. 


3. Draw pictures of thermometers, showing the quick- 
silver at 98°, at 32°, at zero, at 212°, at 70°, at 90°, at 100°: 

4. Draw pictures of thermometers, telling when ice 
melts, when water boils, when the heat is pleasant, how 
warm the body is when one is well, when one has a fever, 
when one has a chill, how warm a bath should be, and how 
low the mercury is when it is very, very cold, below zero. 


5. Why are some music notes called whole notes ? 
half notes? quarter notes? eighth notes ? 

6. What time is it at noon? When does 12 o’clock 
come next ? 


7. How many hours do we spend in school each day ? 


8. Where are the hands on the clock face at the times 
when you go to school morning and afternoon ? 

9. Edgar raised 48 quarts of strawberries. He sold 
zy of them early in the season and +; of them later on. 
How many quarts did he sell at his first sale? How 
many quarts are. ;%, of 48 quarts? ; of 48 quarts? 
4 of 48 quarts? 

1o. A bin contains 32 bushels of corn. The owner took 
out } to be ground into meal and 4 for food for his horses. 
How many bushels in all did he take out ? 


11. Which is the largest angle, an acute, a right, or an 
obtuse angle ? 


STUDY 
COPY 


REVIEWS 
Counting by 3’s. 


A248 (4 6 a7 
11612 -15014-15 16) 17, 


21 22 23 24 25 26 27 28 2 
dl 32 33 34 35 36 37 © 


41 42 43 44 45 46 47 


51 52 53 54 55 56 57 58 5 


61 62 63 64 65 66 67 
F1725(3 f4.Id5 16-17 
81 82 83 84 85 86 87 
91 92 93 94 95 96 97 


Counting by 4’s. 


be oe coy eee LY a ad 


1112 °15 14°15 16 17 
BT e223 24: 20826 27 
31 32 35 34 35 36 

41 42 45 44 45 46 47 
51 52 53 54 55 56 57 
61 62 63 64 65 66 67 
TAVIZs OH 1D 7041 
81 82 83 84 85 86 87 
91 92 93 94 95 96 97 


Counting by 5’s. 


oak Ow Ai; 
14 15 16 17 


on) LO 
— i — 
or) ; oC ht 
DO bo WM bk WH WL CL LO b PO 
— 
oo ws) 


a 
_ 
a 
H Oo 
Oo 


44 45 46 47 
54 55 56 57 
64 65 66 67 
14.75 76.77 
84 85 86 87 
93 94 95 96 97 


> On 
_— 
on 
On 
ot) 


ei lee) C8 | 
== 
COCO 
coOoON OS 
Co tC C&O 


OV & 


23 24 25 26 27 2 
34 35 36 37 


126 


NUMBER TABLES 


Counting by 6's. 


1 P2e Beate tf OOy 
1112 4514515-16 517, 
21 Ze eoree 20020 sed 
31 32 33 34 35 36 37 
41 42 43 44 45 46 47 
D1 52 53 54 55 56 57 
61 62 63 64 65 66 67 
71°72 73 74 75 76 77 
81 82 83 84 85 86 87 
91 92 93.94 95.96 97 


or or 


Ow GSueCr IOx 


Lek 2 ted eaters) a Oe, 
Tiere oat el ogi 
21422 25'24°20 #4 27 


31 32 35 34 35 36 37 : 


41 42 43 44 45 46 47 


d1 52 53 54 55 56 57 | 


61 62 65 64 65 66 67 
71 72 73 74 75 76 77 
81 82 85 84 85 86 87 
91 92 93 94 95 96 97 


Counting by T’s. 


REC ee neti ge hin A 
213814 15 16 17 
2 donot ooP eed, 
31 32 53 34:35 36 37 
41 42 43 44 45 46 47 
51 52 53 54 55 56 57 
61 62 63 64 65 66 67 
11 72 73 (4 75 76 77 
81 82 83 84 85 86 87 


8 9 
18 19 
28 29 


3.9 
18°19 
28 29 
38 39 
48 49 
58 59 
68 69 
78 79 
88 89 


10 
20 
30 
40 
50 
60 
70 
80 
90 


100 


10 
20 
30 
40 
50 
60 
70 


80 


90 


100 


10 
20 
30 
40 
50 
60 
70 
80 
90 


91 92 93 94 95 96 97 98 99 100 


The 10’s are always at the ends of the rows. 


= 


Counting by 9’s. 


73 


— 85 


97 


98 


3 


15 


99 


109 110 111 
121 122 123 
153 134 135 


NUMBER TABLES 1 


4 


100 
112 
124 
136 


9) 
17 
29 


6 
18 
30 
42 
54 
66 
78 
90 


101 102 
115 114 
125 126 
137 138 


Counting by 11’s. 


1 
15 
25 
37 
49 
61 
73 
85 
97 


9 


14 


3 
15 
27 
39 
51 
63 
75 
87 
2h, 


109 110 111 
121 122 123 
133 154 155 


4 


88 
100 
Liz 
124 
136 


ov 


89 


101 102 
115 114 
125 126 


157 138 


79 
91 
103 
115 
127 


159 


91 
103 
115 
121, 


139 


12 


20 


52 


80 
92 
104 


7 


93 
105 


116 117 


128 
140 


80 
92 
104 
116 
128 
140 


129 1: 


141 


93 
105 
ise 
129 
141 


46 
58 
70 
82 
94 


TO 144 


59 
71 
83 


95 


96 


106 107 108 
118 119 120 
130 131 132 
142 143 144 


that 
the 2 figures in 
each number 
which contains 


Notice 


3 9 always add 


together 9, ex- 
cept 99. 9+9 
Notice also that 
the unit figure 
of each larger 
multiple of 9 is 
always 1 less. 
18, 27, 36, and 
so on. 


Notice that 
from 1 to 100 
the 2 figures in 
each multiple of 
11 are always 
the same, and 
that above 100 
the number of 
tens always in- 
creases 1, 110, 
121, and so on, 
and the 
ber of units al- 
ways increases 
1, 121, 182, 148. 


num- 


1. Copy these Number Tables in red and blue pencil on 
paper, or in red and blue chalk on the blackboard. 


2. 


Read these Tables in class, explaining them. 


TESTS OF 128 


SUCCESS 
ORAL 
1. Count by fours to one hundred. 
2. How many are 15—44+8+4943—10—2-7x2=? 
3. How many dimes are there in half a dollar ? 
4. How much is 4 of 4? dof 4? lof 2? 
5. Is 4 more or less than}? } than $? }thand? Why? 
6. Give the multiplication table of threes. 
7. How many pints are there in a gallon? in a peck? 
8. Measure the size of the schoolroom in feet. 
9. Read the calendar for to-day. 


10. Tell a number-story about 24 cents, 4 boys, and two 
dozen apples that cost a dime a dozen. 


WRITTEN 
Teed see eo eee 2. Subtract: 46 92 T4 
eee eee La Lis Eo 
IBS ein <.  oe 


3. Write the Number Table of One Hundred, showing 
very plainly every number containing 7. 

4. Draw a clock face, showing 5.20 o’clock. 

5. Draw a rectangle divided into sixths. 

6. Write in words 2671, 4203, 3081, 1850. 

7, Answer 0+(4x2)=? (8x3)+9=? (18+6)4+7=? 

8. John had one dollar. He spent a quarter for a cap, 
forty cents for a bantam hen, and a nickel for chestnuts. 
How much money did he have left ? 


9. What is the ratio of 6 to 9? of 12 to4? of d to 3? 
10. Write the address of your house and the day of the 
month and week. 


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